Identifier
- St000415: Ordered trees ⟶ ℤ
Values
[[]] => 1
[[],[]] => 2
[[[]]] => 1
[[],[],[]] => 6
[[],[[]]] => 2
[[[]],[]] => 2
[[[],[]]] => 2
[[[[]]]] => 1
[[],[],[],[]] => 24
[[],[],[[]]] => 6
[[],[[]],[]] => 6
[[],[[],[]]] => 4
[[],[[[]]]] => 2
[[[]],[],[]] => 6
[[[]],[[]]] => 2
[[[],[]],[]] => 4
[[[[]]],[]] => 2
[[[],[],[]]] => 6
[[[],[[]]]] => 2
[[[[]],[]]] => 2
[[[[],[]]]] => 2
[[[[[]]]]] => 1
[[],[],[],[],[]] => 120
[[],[],[],[[]]] => 24
[[],[],[[]],[]] => 24
[[],[],[[],[]]] => 12
[[],[],[[[]]]] => 6
[[],[[]],[],[]] => 24
[[],[[]],[[]]] => 6
[[],[[],[]],[]] => 12
[[],[[[]]],[]] => 6
[[],[[],[],[]]] => 12
[[],[[],[[]]]] => 4
[[],[[[]],[]]] => 4
[[],[[[],[]]]] => 4
[[],[[[[]]]]] => 2
[[[]],[],[],[]] => 24
[[[]],[],[[]]] => 6
[[[]],[[]],[]] => 6
[[[]],[[],[]]] => 4
[[[]],[[[]]]] => 2
[[[],[]],[],[]] => 12
[[[[]]],[],[]] => 6
[[[],[]],[[]]] => 4
[[[[]]],[[]]] => 2
[[[],[],[]],[]] => 12
[[[],[[]]],[]] => 4
[[[[]],[]],[]] => 4
[[[[],[]]],[]] => 4
[[[[[]]]],[]] => 2
[[[],[],[],[]]] => 24
[[[],[],[[]]]] => 6
[[[],[[]],[]]] => 6
[[[],[[],[]]]] => 4
[[[],[[[]]]]] => 2
[[[[]],[],[]]] => 6
[[[[]],[[]]]] => 2
[[[[],[]],[]]] => 4
[[[[[]]],[]]] => 2
[[[[],[],[]]]] => 6
[[[[],[[]]]]] => 2
[[[[[]],[]]]] => 2
[[[[[],[]]]]] => 2
[[[[[[]]]]]] => 1
[[],[],[],[],[],[]] => 720
[[],[],[],[],[[]]] => 120
[[],[],[],[[]],[]] => 120
[[],[],[],[[],[]]] => 48
[[],[],[],[[[]]]] => 24
[[],[],[[]],[],[]] => 120
[[],[],[[]],[[]]] => 24
[[],[],[[],[]],[]] => 48
[[],[],[[[]]],[]] => 24
[[],[],[[],[],[]]] => 36
[[],[],[[],[[]]]] => 12
[[],[],[[[]],[]]] => 12
[[],[],[[[],[]]]] => 12
[[],[],[[[[]]]]] => 6
[[],[[]],[],[],[]] => 120
[[],[[]],[],[[]]] => 24
[[],[[]],[[]],[]] => 24
[[],[[]],[[],[]]] => 12
[[],[[]],[[[]]]] => 6
[[],[[],[]],[],[]] => 48
[[],[[[]]],[],[]] => 24
[[],[[],[]],[[]]] => 12
[[],[[[]]],[[]]] => 6
[[],[[],[],[]],[]] => 36
[[],[[],[[]]],[]] => 12
[[],[[[]],[]],[]] => 12
[[],[[[],[]]],[]] => 12
[[],[[[[]]]],[]] => 6
[[],[[],[],[],[]]] => 48
[[],[[],[],[[]]]] => 12
[[],[[],[[]],[]]] => 12
[[],[[],[[],[]]]] => 8
[[],[[],[[[]]]]] => 4
[[],[[[]],[],[]]] => 12
[[],[[[]],[[]]]] => 4
[[],[[[],[]],[]]] => 8
[[],[[[[]]],[]]] => 4
>>> Load all 1200 entries. <<<[[],[[[],[],[]]]] => 12
[[],[[[],[[]]]]] => 4
[[],[[[[]],[]]]] => 4
[[],[[[[],[]]]]] => 4
[[],[[[[[]]]]]] => 2
[[[]],[],[],[],[]] => 120
[[[]],[],[],[[]]] => 24
[[[]],[],[[]],[]] => 24
[[[]],[],[[],[]]] => 12
[[[]],[],[[[]]]] => 6
[[[]],[[]],[],[]] => 24
[[[]],[[]],[[]]] => 6
[[[]],[[],[]],[]] => 12
[[[]],[[[]]],[]] => 6
[[[]],[[],[],[]]] => 12
[[[]],[[],[[]]]] => 4
[[[]],[[[]],[]]] => 4
[[[]],[[[],[]]]] => 4
[[[]],[[[[]]]]] => 2
[[[],[]],[],[],[]] => 48
[[[[]]],[],[],[]] => 24
[[[],[]],[],[[]]] => 12
[[[[]]],[],[[]]] => 6
[[[],[]],[[]],[]] => 12
[[[[]]],[[]],[]] => 6
[[[],[]],[[],[]]] => 8
[[[],[]],[[[]]]] => 4
[[[[]]],[[],[]]] => 4
[[[[]]],[[[]]]] => 2
[[[],[],[]],[],[]] => 36
[[[],[[]]],[],[]] => 12
[[[[]],[]],[],[]] => 12
[[[[],[]]],[],[]] => 12
[[[[[]]]],[],[]] => 6
[[[],[],[]],[[]]] => 12
[[[],[[]]],[[]]] => 4
[[[[]],[]],[[]]] => 4
[[[[],[]]],[[]]] => 4
[[[[[]]]],[[]]] => 2
[[[],[],[],[]],[]] => 48
[[[],[],[[]]],[]] => 12
[[[],[[]],[]],[]] => 12
[[[],[[],[]]],[]] => 8
[[[],[[[]]]],[]] => 4
[[[[]],[],[]],[]] => 12
[[[[]],[[]]],[]] => 4
[[[[],[]],[]],[]] => 8
[[[[[]]],[]],[]] => 4
[[[[],[],[]]],[]] => 12
[[[[],[[]]]],[]] => 4
[[[[[]],[]]],[]] => 4
[[[[[],[]]]],[]] => 4
[[[[[[]]]]],[]] => 2
[[[],[],[],[],[]]] => 120
[[[],[],[],[[]]]] => 24
[[[],[],[[]],[]]] => 24
[[[],[],[[],[]]]] => 12
[[[],[],[[[]]]]] => 6
[[[],[[]],[],[]]] => 24
[[[],[[]],[[]]]] => 6
[[[],[[],[]],[]]] => 12
[[[],[[[]]],[]]] => 6
[[[],[[],[],[]]]] => 12
[[[],[[],[[]]]]] => 4
[[[],[[[]],[]]]] => 4
[[[],[[[],[]]]]] => 4
[[[],[[[[]]]]]] => 2
[[[[]],[],[],[]]] => 24
[[[[]],[],[[]]]] => 6
[[[[]],[[]],[]]] => 6
[[[[]],[[],[]]]] => 4
[[[[]],[[[]]]]] => 2
[[[[],[]],[],[]]] => 12
[[[[[]]],[],[]]] => 6
[[[[],[]],[[]]]] => 4
[[[[[]]],[[]]]] => 2
[[[[],[],[]],[]]] => 12
[[[[],[[]]],[]]] => 4
[[[[[]],[]],[]]] => 4
[[[[[],[]]],[]]] => 4
[[[[[[]]]],[]]] => 2
[[[[],[],[],[]]]] => 24
[[[[],[],[[]]]]] => 6
[[[[],[[]],[]]]] => 6
[[[[],[[],[]]]]] => 4
[[[[],[[[]]]]]] => 2
[[[[[]],[],[]]]] => 6
[[[[[]],[[]]]]] => 2
[[[[[],[]],[]]]] => 4
[[[[[[]]],[]]]] => 2
[[[[[],[],[]]]]] => 6
[[[[[],[[]]]]]] => 2
[[[[[[]],[]]]]] => 2
[[[[[[],[]]]]]] => 2
[[[[[[[]]]]]]] => 1
[[],[],[],[],[],[],[]] => 5040
[[],[],[],[],[],[[]]] => 720
[[],[],[],[],[[]],[]] => 720
[[],[],[],[],[[],[]]] => 240
[[],[],[],[],[[[]]]] => 120
[[],[],[],[[]],[],[]] => 720
[[],[],[],[[]],[[]]] => 120
[[],[],[],[[],[]],[]] => 240
[[],[],[],[[[]]],[]] => 120
[[],[],[],[[],[],[]]] => 144
[[],[],[],[[],[[]]]] => 48
[[],[],[],[[[]],[]]] => 48
[[],[],[],[[[],[]]]] => 48
[[],[],[],[[[[]]]]] => 24
[[],[],[[]],[],[],[]] => 720
[[],[],[[]],[],[[]]] => 120
[[],[],[[]],[[]],[]] => 120
[[],[],[[]],[[],[]]] => 48
[[],[],[[]],[[[]]]] => 24
[[],[],[[],[]],[],[]] => 240
[[],[],[[[]]],[],[]] => 120
[[],[],[[],[]],[[]]] => 48
[[],[],[[[]]],[[]]] => 24
[[],[],[[],[],[]],[]] => 144
[[],[],[[],[[]]],[]] => 48
[[],[],[[[]],[]],[]] => 48
[[],[],[[[],[]]],[]] => 48
[[],[],[[[[]]]],[]] => 24
[[],[],[[],[],[],[]]] => 144
[[],[],[[],[],[[]]]] => 36
[[],[],[[],[[]],[]]] => 36
[[],[],[[],[[],[]]]] => 24
[[],[],[[],[[[]]]]] => 12
[[],[],[[[]],[],[]]] => 36
[[],[],[[[]],[[]]]] => 12
[[],[],[[[],[]],[]]] => 24
[[],[],[[[[]]],[]]] => 12
[[],[],[[[],[],[]]]] => 36
[[],[],[[[],[[]]]]] => 12
[[],[],[[[[]],[]]]] => 12
[[],[],[[[[],[]]]]] => 12
[[],[],[[[[[]]]]]] => 6
[[],[[]],[],[],[],[]] => 720
[[],[[]],[],[],[[]]] => 120
[[],[[]],[],[[]],[]] => 120
[[],[[]],[],[[],[]]] => 48
[[],[[]],[],[[[]]]] => 24
[[],[[]],[[]],[],[]] => 120
[[],[[]],[[]],[[]]] => 24
[[],[[]],[[],[]],[]] => 48
[[],[[]],[[[]]],[]] => 24
[[],[[]],[[],[],[]]] => 36
[[],[[]],[[],[[]]]] => 12
[[],[[]],[[[]],[]]] => 12
[[],[[]],[[[],[]]]] => 12
[[],[[]],[[[[]]]]] => 6
[[],[[],[]],[],[],[]] => 240
[[],[[[]]],[],[],[]] => 120
[[],[[],[]],[],[[]]] => 48
[[],[[[]]],[],[[]]] => 24
[[],[[],[]],[[]],[]] => 48
[[],[[[]]],[[]],[]] => 24
[[],[[],[]],[[],[]]] => 24
[[],[[],[]],[[[]]]] => 12
[[],[[[]]],[[],[]]] => 12
[[],[[[]]],[[[]]]] => 6
[[],[[],[],[]],[],[]] => 144
[[],[[],[[]]],[],[]] => 48
[[],[[[]],[]],[],[]] => 48
[[],[[[],[]]],[],[]] => 48
[[],[[[[]]]],[],[]] => 24
[[],[[],[],[]],[[]]] => 36
[[],[[],[[]]],[[]]] => 12
[[],[[[]],[]],[[]]] => 12
[[],[[[],[]]],[[]]] => 12
[[],[[[[]]]],[[]]] => 6
[[],[[],[],[],[]],[]] => 144
[[],[[],[],[[]]],[]] => 36
[[],[[],[[]],[]],[]] => 36
[[],[[],[[],[]]],[]] => 24
[[],[[],[[[]]]],[]] => 12
[[],[[[]],[],[]],[]] => 36
[[],[[[]],[[]]],[]] => 12
[[],[[[],[]],[]],[]] => 24
[[],[[[[]]],[]],[]] => 12
[[],[[[],[],[]]],[]] => 36
[[],[[[],[[]]]],[]] => 12
[[],[[[[]],[]]],[]] => 12
[[],[[[[],[]]]],[]] => 12
[[],[[[[[]]]]],[]] => 6
[[],[[],[],[],[],[]]] => 240
[[],[[],[],[],[[]]]] => 48
[[],[[],[],[[]],[]]] => 48
[[],[[],[],[[],[]]]] => 24
[[],[[],[],[[[]]]]] => 12
[[],[[],[[]],[],[]]] => 48
[[],[[],[[]],[[]]]] => 12
[[],[[],[[],[]],[]]] => 24
[[],[[],[[[]]],[]]] => 12
[[],[[],[[],[],[]]]] => 24
[[],[[],[[],[[]]]]] => 8
[[],[[],[[[]],[]]]] => 8
[[],[[],[[[],[]]]]] => 8
[[],[[],[[[[]]]]]] => 4
[[],[[[]],[],[],[]]] => 48
[[],[[[]],[],[[]]]] => 12
[[],[[[]],[[]],[]]] => 12
[[],[[[]],[[],[]]]] => 8
[[],[[[]],[[[]]]]] => 4
[[],[[[],[]],[],[]]] => 24
[[],[[[[]]],[],[]]] => 12
[[],[[[],[]],[[]]]] => 8
[[],[[[[]]],[[]]]] => 4
[[],[[[],[],[]],[]]] => 24
[[],[[[],[[]]],[]]] => 8
[[],[[[[]],[]],[]]] => 8
[[],[[[[],[]]],[]]] => 8
[[],[[[[[]]]],[]]] => 4
[[],[[[],[],[],[]]]] => 48
[[],[[[],[],[[]]]]] => 12
[[],[[[],[[]],[]]]] => 12
[[],[[[],[[],[]]]]] => 8
[[],[[[],[[[]]]]]] => 4
[[],[[[[]],[],[]]]] => 12
[[],[[[[]],[[]]]]] => 4
[[],[[[[],[]],[]]]] => 8
[[],[[[[[]]],[]]]] => 4
[[],[[[[],[],[]]]]] => 12
[[],[[[[],[[]]]]]] => 4
[[],[[[[[]],[]]]]] => 4
[[],[[[[[],[]]]]]] => 4
[[],[[[[[[]]]]]]] => 2
[[[]],[],[],[],[],[]] => 720
[[[]],[],[],[],[[]]] => 120
[[[]],[],[],[[]],[]] => 120
[[[]],[],[],[[],[]]] => 48
[[[]],[],[],[[[]]]] => 24
[[[]],[],[[]],[],[]] => 120
[[[]],[],[[]],[[]]] => 24
[[[]],[],[[],[]],[]] => 48
[[[]],[],[[[]]],[]] => 24
[[[]],[],[[],[],[]]] => 36
[[[]],[],[[],[[]]]] => 12
[[[]],[],[[[]],[]]] => 12
[[[]],[],[[[],[]]]] => 12
[[[]],[],[[[[]]]]] => 6
[[[]],[[]],[],[],[]] => 120
[[[]],[[]],[],[[]]] => 24
[[[]],[[]],[[]],[]] => 24
[[[]],[[]],[[],[]]] => 12
[[[]],[[]],[[[]]]] => 6
[[[]],[[],[]],[],[]] => 48
[[[]],[[[]]],[],[]] => 24
[[[]],[[],[]],[[]]] => 12
[[[]],[[[]]],[[]]] => 6
[[[]],[[],[],[]],[]] => 36
[[[]],[[],[[]]],[]] => 12
[[[]],[[[]],[]],[]] => 12
[[[]],[[[],[]]],[]] => 12
[[[]],[[[[]]]],[]] => 6
[[[]],[[],[],[],[]]] => 48
[[[]],[[],[],[[]]]] => 12
[[[]],[[],[[]],[]]] => 12
[[[]],[[],[[],[]]]] => 8
[[[]],[[],[[[]]]]] => 4
[[[]],[[[]],[],[]]] => 12
[[[]],[[[]],[[]]]] => 4
[[[]],[[[],[]],[]]] => 8
[[[]],[[[[]]],[]]] => 4
[[[]],[[[],[],[]]]] => 12
[[[]],[[[],[[]]]]] => 4
[[[]],[[[[]],[]]]] => 4
[[[]],[[[[],[]]]]] => 4
[[[]],[[[[[]]]]]] => 2
[[[],[]],[],[],[],[]] => 240
[[[[]]],[],[],[],[]] => 120
[[[],[]],[],[],[[]]] => 48
[[[[]]],[],[],[[]]] => 24
[[[],[]],[],[[]],[]] => 48
[[[[]]],[],[[]],[]] => 24
[[[],[]],[],[[],[]]] => 24
[[[],[]],[],[[[]]]] => 12
[[[[]]],[],[[],[]]] => 12
[[[[]]],[],[[[]]]] => 6
[[[],[]],[[]],[],[]] => 48
[[[[]]],[[]],[],[]] => 24
[[[],[]],[[]],[[]]] => 12
[[[[]]],[[]],[[]]] => 6
[[[],[]],[[],[]],[]] => 24
[[[],[]],[[[]]],[]] => 12
[[[[]]],[[],[]],[]] => 12
[[[[]]],[[[]]],[]] => 6
[[[],[]],[[],[],[]]] => 24
[[[],[]],[[],[[]]]] => 8
[[[],[]],[[[]],[]]] => 8
[[[],[]],[[[],[]]]] => 8
[[[],[]],[[[[]]]]] => 4
[[[[]]],[[],[],[]]] => 12
[[[[]]],[[],[[]]]] => 4
[[[[]]],[[[]],[]]] => 4
[[[[]]],[[[],[]]]] => 4
[[[[]]],[[[[]]]]] => 2
[[[],[],[]],[],[],[]] => 144
[[[],[[]]],[],[],[]] => 48
[[[[]],[]],[],[],[]] => 48
[[[[],[]]],[],[],[]] => 48
[[[[[]]]],[],[],[]] => 24
[[[],[],[]],[],[[]]] => 36
[[[],[[]]],[],[[]]] => 12
[[[[]],[]],[],[[]]] => 12
[[[[],[]]],[],[[]]] => 12
[[[[[]]]],[],[[]]] => 6
[[[],[],[]],[[]],[]] => 36
[[[],[[]]],[[]],[]] => 12
[[[[]],[]],[[]],[]] => 12
[[[[],[]]],[[]],[]] => 12
[[[[[]]]],[[]],[]] => 6
[[[],[],[]],[[],[]]] => 24
[[[],[],[]],[[[]]]] => 12
[[[],[[]]],[[],[]]] => 8
[[[],[[]]],[[[]]]] => 4
[[[[]],[]],[[],[]]] => 8
[[[[]],[]],[[[]]]] => 4
[[[[],[]]],[[],[]]] => 8
[[[[],[]]],[[[]]]] => 4
[[[[[]]]],[[],[]]] => 4
[[[[[]]]],[[[]]]] => 2
[[[],[],[],[]],[],[]] => 144
[[[],[],[[]]],[],[]] => 36
[[[],[[]],[]],[],[]] => 36
[[[],[[],[]]],[],[]] => 24
[[[],[[[]]]],[],[]] => 12
[[[[]],[],[]],[],[]] => 36
[[[[]],[[]]],[],[]] => 12
[[[[],[]],[]],[],[]] => 24
[[[[[]]],[]],[],[]] => 12
[[[[],[],[]]],[],[]] => 36
[[[[],[[]]]],[],[]] => 12
[[[[[]],[]]],[],[]] => 12
[[[[[],[]]]],[],[]] => 12
[[[[[[]]]]],[],[]] => 6
[[[],[],[],[]],[[]]] => 48
[[[],[],[[]]],[[]]] => 12
[[[],[[]],[]],[[]]] => 12
[[[],[[],[]]],[[]]] => 8
[[[],[[[]]]],[[]]] => 4
[[[[]],[],[]],[[]]] => 12
[[[[]],[[]]],[[]]] => 4
[[[[],[]],[]],[[]]] => 8
[[[[[]]],[]],[[]]] => 4
[[[[],[],[]]],[[]]] => 12
[[[[],[[]]]],[[]]] => 4
[[[[[]],[]]],[[]]] => 4
[[[[[],[]]]],[[]]] => 4
[[[[[[]]]]],[[]]] => 2
[[[],[],[],[],[]],[]] => 240
[[[],[],[],[[]]],[]] => 48
[[[],[],[[]],[]],[]] => 48
[[[],[],[[],[]]],[]] => 24
[[[],[],[[[]]]],[]] => 12
[[[],[[]],[],[]],[]] => 48
[[[],[[]],[[]]],[]] => 12
[[[],[[],[]],[]],[]] => 24
[[[],[[[]]],[]],[]] => 12
[[[],[[],[],[]]],[]] => 24
[[[],[[],[[]]]],[]] => 8
[[[],[[[]],[]]],[]] => 8
[[[],[[[],[]]]],[]] => 8
[[[],[[[[]]]]],[]] => 4
[[[[]],[],[],[]],[]] => 48
[[[[]],[],[[]]],[]] => 12
[[[[]],[[]],[]],[]] => 12
[[[[]],[[],[]]],[]] => 8
[[[[]],[[[]]]],[]] => 4
[[[[],[]],[],[]],[]] => 24
[[[[[]]],[],[]],[]] => 12
[[[[],[]],[[]]],[]] => 8
[[[[[]]],[[]]],[]] => 4
[[[[],[],[]],[]],[]] => 24
[[[[],[[]]],[]],[]] => 8
[[[[[]],[]],[]],[]] => 8
[[[[[],[]]],[]],[]] => 8
[[[[[[]]]],[]],[]] => 4
[[[[],[],[],[]]],[]] => 48
[[[[],[],[[]]]],[]] => 12
[[[[],[[]],[]]],[]] => 12
[[[[],[[],[]]]],[]] => 8
[[[[],[[[]]]]],[]] => 4
[[[[[]],[],[]]],[]] => 12
[[[[[]],[[]]]],[]] => 4
[[[[[],[]],[]]],[]] => 8
[[[[[[]]],[]]],[]] => 4
[[[[[],[],[]]]],[]] => 12
[[[[[],[[]]]]],[]] => 4
[[[[[[]],[]]]],[]] => 4
[[[[[[],[]]]]],[]] => 4
[[[[[[[]]]]]],[]] => 2
[[[],[],[],[],[],[]]] => 720
[[[],[],[],[],[[]]]] => 120
[[[],[],[],[[]],[]]] => 120
[[[],[],[],[[],[]]]] => 48
[[[],[],[],[[[]]]]] => 24
[[[],[],[[]],[],[]]] => 120
[[[],[],[[]],[[]]]] => 24
[[[],[],[[],[]],[]]] => 48
[[[],[],[[[]]],[]]] => 24
[[[],[],[[],[],[]]]] => 36
[[[],[],[[],[[]]]]] => 12
[[[],[],[[[]],[]]]] => 12
[[[],[],[[[],[]]]]] => 12
[[[],[],[[[[]]]]]] => 6
[[[],[[]],[],[],[]]] => 120
[[[],[[]],[],[[]]]] => 24
[[[],[[]],[[]],[]]] => 24
[[[],[[]],[[],[]]]] => 12
[[[],[[]],[[[]]]]] => 6
[[[],[[],[]],[],[]]] => 48
[[[],[[[]]],[],[]]] => 24
[[[],[[],[]],[[]]]] => 12
[[[],[[[]]],[[]]]] => 6
[[[],[[],[],[]],[]]] => 36
[[[],[[],[[]]],[]]] => 12
[[[],[[[]],[]],[]]] => 12
[[[],[[[],[]]],[]]] => 12
[[[],[[[[]]]],[]]] => 6
[[[],[[],[],[],[]]]] => 48
[[[],[[],[],[[]]]]] => 12
[[[],[[],[[]],[]]]] => 12
[[[],[[],[[],[]]]]] => 8
[[[],[[],[[[]]]]]] => 4
[[[],[[[]],[],[]]]] => 12
[[[],[[[]],[[]]]]] => 4
[[[],[[[],[]],[]]]] => 8
[[[],[[[[]]],[]]]] => 4
[[[],[[[],[],[]]]]] => 12
[[[],[[[],[[]]]]]] => 4
[[[],[[[[]],[]]]]] => 4
[[[],[[[[],[]]]]]] => 4
[[[],[[[[[]]]]]]] => 2
[[[[]],[],[],[],[]]] => 120
[[[[]],[],[],[[]]]] => 24
[[[[]],[],[[]],[]]] => 24
[[[[]],[],[[],[]]]] => 12
[[[[]],[],[[[]]]]] => 6
[[[[]],[[]],[],[]]] => 24
[[[[]],[[]],[[]]]] => 6
[[[[]],[[],[]],[]]] => 12
[[[[]],[[[]]],[]]] => 6
[[[[]],[[],[],[]]]] => 12
[[[[]],[[],[[]]]]] => 4
[[[[]],[[[]],[]]]] => 4
[[[[]],[[[],[]]]]] => 4
[[[[]],[[[[]]]]]] => 2
[[[[],[]],[],[],[]]] => 48
[[[[[]]],[],[],[]]] => 24
[[[[],[]],[],[[]]]] => 12
[[[[[]]],[],[[]]]] => 6
[[[[],[]],[[]],[]]] => 12
[[[[[]]],[[]],[]]] => 6
[[[[],[]],[[],[]]]] => 8
[[[[],[]],[[[]]]]] => 4
[[[[[]]],[[],[]]]] => 4
[[[[[]]],[[[]]]]] => 2
[[[[],[],[]],[],[]]] => 36
[[[[],[[]]],[],[]]] => 12
[[[[[]],[]],[],[]]] => 12
[[[[[],[]]],[],[]]] => 12
[[[[[[]]]],[],[]]] => 6
[[[[],[],[]],[[]]]] => 12
[[[[],[[]]],[[]]]] => 4
[[[[[]],[]],[[]]]] => 4
[[[[[],[]]],[[]]]] => 4
[[[[[[]]]],[[]]]] => 2
[[[[],[],[],[]],[]]] => 48
[[[[],[],[[]]],[]]] => 12
[[[[],[[]],[]],[]]] => 12
[[[[],[[],[]]],[]]] => 8
[[[[],[[[]]]],[]]] => 4
[[[[[]],[],[]],[]]] => 12
[[[[[]],[[]]],[]]] => 4
[[[[[],[]],[]],[]]] => 8
[[[[[[]]],[]],[]]] => 4
[[[[[],[],[]]],[]]] => 12
[[[[[],[[]]]],[]]] => 4
[[[[[[]],[]]],[]]] => 4
[[[[[[],[]]]],[]]] => 4
[[[[[[[]]]]],[]]] => 2
[[[[],[],[],[],[]]]] => 120
[[[[],[],[],[[]]]]] => 24
[[[[],[],[[]],[]]]] => 24
[[[[],[],[[],[]]]]] => 12
[[[[],[],[[[]]]]]] => 6
[[[[],[[]],[],[]]]] => 24
[[[[],[[]],[[]]]]] => 6
[[[[],[[],[]],[]]]] => 12
[[[[],[[[]]],[]]]] => 6
[[[[],[[],[],[]]]]] => 12
[[[[],[[],[[]]]]]] => 4
[[[[],[[[]],[]]]]] => 4
[[[[],[[[],[]]]]]] => 4
[[[[],[[[[]]]]]]] => 2
[[[[[]],[],[],[]]]] => 24
[[[[[]],[],[[]]]]] => 6
[[[[[]],[[]],[]]]] => 6
[[[[[]],[[],[]]]]] => 4
[[[[[]],[[[]]]]]] => 2
[[[[[],[]],[],[]]]] => 12
[[[[[[]]],[],[]]]] => 6
[[[[[],[]],[[]]]]] => 4
[[[[[[]]],[[]]]]] => 2
[[[[[],[],[]],[]]]] => 12
[[[[[],[[]]],[]]]] => 4
[[[[[[]],[]],[]]]] => 4
[[[[[[],[]]],[]]]] => 4
[[[[[[[]]]],[]]]] => 2
[[[[[],[],[],[]]]]] => 24
[[[[[],[],[[]]]]]] => 6
[[[[[],[[]],[]]]]] => 6
[[[[[],[[],[]]]]]] => 4
[[[[[],[[[]]]]]]] => 2
[[[[[[]],[],[]]]]] => 6
[[[[[[]],[[]]]]]] => 2
[[[[[[],[]],[]]]]] => 4
[[[[[[[]]],[]]]]] => 2
[[[[[[],[],[]]]]]] => 6
[[[[[[],[[]]]]]]] => 2
[[[[[[[]],[]]]]]] => 2
[[[[[[[],[]]]]]]] => 2
[[[[[[[[]]]]]]]] => 1
[[],[],[],[],[],[],[],[]] => 40320
[[],[],[],[],[],[],[[]]] => 5040
[[],[],[],[],[],[[]],[]] => 5040
[[],[],[],[],[],[[],[]]] => 1440
[[],[],[],[],[],[[[]]]] => 720
[[],[],[],[],[[]],[],[]] => 5040
[[],[],[],[],[[]],[[]]] => 720
[[],[],[],[],[[],[]],[]] => 1440
[[],[],[],[],[[[]]],[]] => 720
[[],[],[],[],[[],[],[]]] => 720
[[],[],[],[],[[],[[]]]] => 240
[[],[],[],[],[[[]],[]]] => 240
[[],[],[],[],[[[],[]]]] => 240
[[],[],[],[],[[[[]]]]] => 120
[[],[],[],[[]],[],[],[]] => 5040
[[],[],[],[[]],[],[[]]] => 720
[[],[],[],[[]],[[]],[]] => 720
[[],[],[],[[]],[[],[]]] => 240
[[],[],[],[[]],[[[]]]] => 120
[[],[],[],[[],[]],[],[]] => 1440
[[],[],[],[[[]]],[],[]] => 720
[[],[],[],[[],[]],[[]]] => 240
[[],[],[],[[[]]],[[]]] => 120
[[],[],[],[[],[],[]],[]] => 720
[[],[],[],[[],[[]]],[]] => 240
[[],[],[],[[[]],[]],[]] => 240
[[],[],[],[[[],[]]],[]] => 240
[[],[],[],[[[[]]]],[]] => 120
[[],[],[],[[],[],[],[]]] => 576
[[],[],[],[[],[],[[]]]] => 144
[[],[],[],[[],[[]],[]]] => 144
[[],[],[],[[],[[],[]]]] => 96
[[],[],[],[[],[[[]]]]] => 48
[[],[],[],[[[]],[],[]]] => 144
[[],[],[],[[[]],[[]]]] => 48
[[],[],[],[[[],[]],[]]] => 96
[[],[],[],[[[[]]],[]]] => 48
[[],[],[],[[[],[],[]]]] => 144
[[],[],[],[[[],[[]]]]] => 48
[[],[],[],[[[[]],[]]]] => 48
[[],[],[],[[[[],[]]]]] => 48
[[],[],[],[[[[[]]]]]] => 24
[[],[],[[]],[],[],[],[]] => 5040
[[],[],[[]],[],[],[[]]] => 720
[[],[],[[]],[],[[]],[]] => 720
[[],[],[[]],[],[[],[]]] => 240
[[],[],[[]],[],[[[]]]] => 120
[[],[],[[]],[[]],[],[]] => 720
[[],[],[[]],[[]],[[]]] => 120
[[],[],[[]],[[],[]],[]] => 240
[[],[],[[]],[[[]]],[]] => 120
[[],[],[[]],[[],[],[]]] => 144
[[],[],[[]],[[],[[]]]] => 48
[[],[],[[]],[[[]],[]]] => 48
[[],[],[[]],[[[],[]]]] => 48
[[],[],[[]],[[[[]]]]] => 24
[[],[],[[],[]],[],[],[]] => 1440
[[],[],[[[]]],[],[],[]] => 720
[[],[],[[],[]],[],[[]]] => 240
[[],[],[[[]]],[],[[]]] => 120
[[],[],[[],[]],[[]],[]] => 240
[[],[],[[[]]],[[]],[]] => 120
[[],[],[[],[]],[[],[]]] => 96
[[],[],[[],[]],[[[]]]] => 48
[[],[],[[[]]],[[],[]]] => 48
[[],[],[[[]]],[[[]]]] => 24
[[],[],[[],[],[]],[],[]] => 720
[[],[],[[],[[]]],[],[]] => 240
[[],[],[[[]],[]],[],[]] => 240
[[],[],[[[],[]]],[],[]] => 240
[[],[],[[[[]]]],[],[]] => 120
[[],[],[[],[],[]],[[]]] => 144
[[],[],[[],[[]]],[[]]] => 48
[[],[],[[[]],[]],[[]]] => 48
[[],[],[[[],[]]],[[]]] => 48
[[],[],[[[[]]]],[[]]] => 24
[[],[],[[],[],[],[]],[]] => 576
[[],[],[[],[],[[]]],[]] => 144
[[],[],[[],[[]],[]],[]] => 144
[[],[],[[],[[],[]]],[]] => 96
[[],[],[[],[[[]]]],[]] => 48
[[],[],[[[]],[],[]],[]] => 144
[[],[],[[[]],[[]]],[]] => 48
[[],[],[[[],[]],[]],[]] => 96
[[],[],[[[[]]],[]],[]] => 48
[[],[],[[[],[],[]]],[]] => 144
[[],[],[[[],[[]]]],[]] => 48
[[],[],[[[[]],[]]],[]] => 48
[[],[],[[[[],[]]]],[]] => 48
[[],[],[[[[[]]]]],[]] => 24
[[],[],[[],[],[],[],[]]] => 720
[[],[],[[],[],[],[[]]]] => 144
[[],[],[[],[],[[]],[]]] => 144
[[],[],[[],[],[[],[]]]] => 72
[[],[],[[],[],[[[]]]]] => 36
[[],[],[[],[[]],[],[]]] => 144
[[],[],[[],[[]],[[]]]] => 36
[[],[],[[],[[],[]],[]]] => 72
[[],[],[[],[[[]]],[]]] => 36
[[],[],[[],[[],[],[]]]] => 72
[[],[],[[],[[],[[]]]]] => 24
[[],[],[[],[[[]],[]]]] => 24
[[],[],[[],[[[],[]]]]] => 24
[[],[],[[],[[[[]]]]]] => 12
[[],[],[[[]],[],[],[]]] => 144
[[],[],[[[]],[],[[]]]] => 36
[[],[],[[[]],[[]],[]]] => 36
[[],[],[[[]],[[],[]]]] => 24
[[],[],[[[]],[[[]]]]] => 12
[[],[],[[[],[]],[],[]]] => 72
[[],[],[[[[]]],[],[]]] => 36
[[],[],[[[],[]],[[]]]] => 24
[[],[],[[[[]]],[[]]]] => 12
[[],[],[[[],[],[]],[]]] => 72
[[],[],[[[],[[]]],[]]] => 24
[[],[],[[[[]],[]],[]]] => 24
[[],[],[[[[],[]]],[]]] => 24
[[],[],[[[[[]]]],[]]] => 12
[[],[],[[[],[],[],[]]]] => 144
[[],[],[[[],[],[[]]]]] => 36
[[],[],[[[],[[]],[]]]] => 36
[[],[],[[[],[[],[]]]]] => 24
[[],[],[[[],[[[]]]]]] => 12
[[],[],[[[[]],[],[]]]] => 36
[[],[],[[[[]],[[]]]]] => 12
[[],[],[[[[],[]],[]]]] => 24
[[],[],[[[[[]]],[]]]] => 12
[[],[],[[[[],[],[]]]]] => 36
[[],[],[[[[],[[]]]]]] => 12
[[],[],[[[[[]],[]]]]] => 12
[[],[],[[[[[],[]]]]]] => 12
[[],[],[[[[[[]]]]]]] => 6
[[],[[]],[],[],[],[],[]] => 5040
[[],[[]],[],[],[],[[]]] => 720
[[],[[]],[],[],[[]],[]] => 720
[[],[[]],[],[],[[],[]]] => 240
[[],[[]],[],[],[[[]]]] => 120
[[],[[]],[],[[]],[],[]] => 720
[[],[[]],[],[[]],[[]]] => 120
[[],[[]],[],[[],[]],[]] => 240
[[],[[]],[],[[[]]],[]] => 120
[[],[[]],[],[[],[],[]]] => 144
[[],[[]],[],[[],[[]]]] => 48
[[],[[]],[],[[[]],[]]] => 48
[[],[[]],[],[[[],[]]]] => 48
[[],[[]],[],[[[[]]]]] => 24
[[],[[]],[[]],[],[],[]] => 720
[[],[[]],[[]],[],[[]]] => 120
[[],[[]],[[]],[[]],[]] => 120
[[],[[]],[[]],[[],[]]] => 48
[[],[[]],[[]],[[[]]]] => 24
[[],[[]],[[],[]],[],[]] => 240
[[],[[]],[[[]]],[],[]] => 120
[[],[[]],[[],[]],[[]]] => 48
[[],[[]],[[[]]],[[]]] => 24
[[],[[]],[[],[],[]],[]] => 144
[[],[[]],[[],[[]]],[]] => 48
[[],[[]],[[[]],[]],[]] => 48
[[],[[]],[[[],[]]],[]] => 48
[[],[[]],[[[[]]]],[]] => 24
[[],[[]],[[],[],[],[]]] => 144
[[],[[]],[[],[],[[]]]] => 36
[[],[[]],[[],[[]],[]]] => 36
[[],[[]],[[],[[],[]]]] => 24
[[],[[]],[[],[[[]]]]] => 12
[[],[[]],[[[]],[],[]]] => 36
[[],[[]],[[[]],[[]]]] => 12
[[],[[]],[[[],[]],[]]] => 24
[[],[[]],[[[[]]],[]]] => 12
[[],[[]],[[[],[],[]]]] => 36
[[],[[]],[[[],[[]]]]] => 12
[[],[[]],[[[[]],[]]]] => 12
[[],[[]],[[[[],[]]]]] => 12
[[],[[]],[[[[[]]]]]] => 6
[[],[[],[]],[],[],[],[]] => 1440
[[],[[[]]],[],[],[],[]] => 720
[[],[[],[]],[],[],[[]]] => 240
[[],[[[]]],[],[],[[]]] => 120
[[],[[],[]],[],[[]],[]] => 240
[[],[[[]]],[],[[]],[]] => 120
[[],[[],[]],[],[[],[]]] => 96
[[],[[],[]],[],[[[]]]] => 48
[[],[[[]]],[],[[],[]]] => 48
[[],[[[]]],[],[[[]]]] => 24
[[],[[],[]],[[]],[],[]] => 240
[[],[[[]]],[[]],[],[]] => 120
[[],[[],[]],[[]],[[]]] => 48
[[],[[[]]],[[]],[[]]] => 24
[[],[[],[]],[[],[]],[]] => 96
[[],[[],[]],[[[]]],[]] => 48
[[],[[[]]],[[],[]],[]] => 48
[[],[[[]]],[[[]]],[]] => 24
[[],[[],[]],[[],[],[]]] => 72
[[],[[],[]],[[],[[]]]] => 24
[[],[[],[]],[[[]],[]]] => 24
[[],[[],[]],[[[],[]]]] => 24
[[],[[],[]],[[[[]]]]] => 12
[[],[[[]]],[[],[],[]]] => 36
[[],[[[]]],[[],[[]]]] => 12
[[],[[[]]],[[[]],[]]] => 12
[[],[[[]]],[[[],[]]]] => 12
[[],[[[]]],[[[[]]]]] => 6
[[],[[],[],[]],[],[],[]] => 720
[[],[[],[[]]],[],[],[]] => 240
[[],[[[]],[]],[],[],[]] => 240
[[],[[[],[]]],[],[],[]] => 240
[[],[[[[]]]],[],[],[]] => 120
[[],[[],[],[]],[],[[]]] => 144
[[],[[],[[]]],[],[[]]] => 48
[[],[[[]],[]],[],[[]]] => 48
[[],[[[],[]]],[],[[]]] => 48
[[],[[[[]]]],[],[[]]] => 24
[[],[[],[],[]],[[]],[]] => 144
[[],[[],[[]]],[[]],[]] => 48
[[],[[[]],[]],[[]],[]] => 48
[[],[[[],[]]],[[]],[]] => 48
[[],[[[[]]]],[[]],[]] => 24
[[],[[],[],[]],[[],[]]] => 72
[[],[[],[],[]],[[[]]]] => 36
[[],[[],[[]]],[[],[]]] => 24
[[],[[],[[]]],[[[]]]] => 12
[[],[[[]],[]],[[],[]]] => 24
[[],[[[]],[]],[[[]]]] => 12
[[],[[[],[]]],[[],[]]] => 24
[[],[[[],[]]],[[[]]]] => 12
[[],[[[[]]]],[[],[]]] => 12
[[],[[[[]]]],[[[]]]] => 6
[[],[[],[],[],[]],[],[]] => 576
[[],[[],[],[[]]],[],[]] => 144
[[],[[],[[]],[]],[],[]] => 144
[[],[[],[[],[]]],[],[]] => 96
[[],[[],[[[]]]],[],[]] => 48
[[],[[[]],[],[]],[],[]] => 144
[[],[[[]],[[]]],[],[]] => 48
[[],[[[],[]],[]],[],[]] => 96
[[],[[[[]]],[]],[],[]] => 48
[[],[[[],[],[]]],[],[]] => 144
[[],[[[],[[]]]],[],[]] => 48
[[],[[[[]],[]]],[],[]] => 48
[[],[[[[],[]]]],[],[]] => 48
[[],[[[[[]]]]],[],[]] => 24
[[],[[],[],[],[]],[[]]] => 144
[[],[[],[],[[]]],[[]]] => 36
[[],[[],[[]],[]],[[]]] => 36
[[],[[],[[],[]]],[[]]] => 24
[[],[[],[[[]]]],[[]]] => 12
[[],[[[]],[],[]],[[]]] => 36
[[],[[[]],[[]]],[[]]] => 12
[[],[[[],[]],[]],[[]]] => 24
[[],[[[[]]],[]],[[]]] => 12
[[],[[[],[],[]]],[[]]] => 36
[[],[[[],[[]]]],[[]]] => 12
[[],[[[[]],[]]],[[]]] => 12
[[],[[[[],[]]]],[[]]] => 12
[[],[[[[[]]]]],[[]]] => 6
[[],[[],[],[],[],[]],[]] => 720
[[],[[],[],[],[[]]],[]] => 144
[[],[[],[],[[]],[]],[]] => 144
[[],[[],[],[[],[]]],[]] => 72
[[],[[],[],[[[]]]],[]] => 36
[[],[[],[[]],[],[]],[]] => 144
[[],[[],[[]],[[]]],[]] => 36
[[],[[],[[],[]],[]],[]] => 72
[[],[[],[[[]]],[]],[]] => 36
[[],[[],[[],[],[]]],[]] => 72
[[],[[],[[],[[]]]],[]] => 24
[[],[[],[[[]],[]]],[]] => 24
[[],[[],[[[],[]]]],[]] => 24
[[],[[],[[[[]]]]],[]] => 12
[[],[[[]],[],[],[]],[]] => 144
[[],[[[]],[],[[]]],[]] => 36
[[],[[[]],[[]],[]],[]] => 36
[[],[[[]],[[],[]]],[]] => 24
[[],[[[]],[[[]]]],[]] => 12
[[],[[[],[]],[],[]],[]] => 72
[[],[[[[]]],[],[]],[]] => 36
[[],[[[],[]],[[]]],[]] => 24
[[],[[[[]]],[[]]],[]] => 12
[[],[[[],[],[]],[]],[]] => 72
[[],[[[],[[]]],[]],[]] => 24
[[],[[[[]],[]],[]],[]] => 24
[[],[[[[],[]]],[]],[]] => 24
[[],[[[[[]]]],[]],[]] => 12
[[],[[[],[],[],[]]],[]] => 144
[[],[[[],[],[[]]]],[]] => 36
[[],[[[],[[]],[]]],[]] => 36
[[],[[[],[[],[]]]],[]] => 24
[[],[[[],[[[]]]]],[]] => 12
[[],[[[[]],[],[]]],[]] => 36
[[],[[[[]],[[]]]],[]] => 12
[[],[[[[],[]],[]]],[]] => 24
[[],[[[[[]]],[]]],[]] => 12
[[],[[[[],[],[]]]],[]] => 36
[[],[[[[],[[]]]]],[]] => 12
[[],[[[[[]],[]]]],[]] => 12
[[],[[[[[],[]]]]],[]] => 12
[[],[[[[[[]]]]]],[]] => 6
[[],[[],[],[],[],[],[]]] => 1440
[[],[[],[],[],[],[[]]]] => 240
[[],[[],[],[],[[]],[]]] => 240
[[],[[],[],[],[[],[]]]] => 96
[[],[[],[],[],[[[]]]]] => 48
[[],[[],[],[[]],[],[]]] => 240
[[],[[],[],[[]],[[]]]] => 48
[[],[[],[],[[],[]],[]]] => 96
[[],[[],[],[[[]]],[]]] => 48
[[],[[],[],[[],[],[]]]] => 72
[[],[[],[],[[],[[]]]]] => 24
[[],[[],[],[[[]],[]]]] => 24
[[],[[],[],[[[],[]]]]] => 24
[[],[[],[],[[[[]]]]]] => 12
[[],[[],[[]],[],[],[]]] => 240
[[],[[],[[]],[],[[]]]] => 48
[[],[[],[[]],[[]],[]]] => 48
[[],[[],[[]],[[],[]]]] => 24
[[],[[],[[]],[[[]]]]] => 12
[[],[[],[[],[]],[],[]]] => 96
[[],[[],[[[]]],[],[]]] => 48
[[],[[],[[],[]],[[]]]] => 24
[[],[[],[[[]]],[[]]]] => 12
[[],[[],[[],[],[]],[]]] => 72
[[],[[],[[],[[]]],[]]] => 24
[[],[[],[[[]],[]],[]]] => 24
[[],[[],[[[],[]]],[]]] => 24
[[],[[],[[[[]]]],[]]] => 12
[[],[[],[[],[],[],[]]]] => 96
[[],[[],[[],[],[[]]]]] => 24
[[],[[],[[],[[]],[]]]] => 24
[[],[[],[[],[[],[]]]]] => 16
[[],[[],[[],[[[]]]]]] => 8
[[],[[],[[[]],[],[]]]] => 24
[[],[[],[[[]],[[]]]]] => 8
[[],[[],[[[],[]],[]]]] => 16
[[],[[],[[[[]]],[]]]] => 8
[[],[[],[[[],[],[]]]]] => 24
[[],[[],[[[],[[]]]]]] => 8
[[],[[],[[[[]],[]]]]] => 8
[[],[[],[[[[],[]]]]]] => 8
[[],[[],[[[[[]]]]]]] => 4
[[],[[[]],[],[],[],[]]] => 240
[[],[[[]],[],[],[[]]]] => 48
[[],[[[]],[],[[]],[]]] => 48
[[],[[[]],[],[[],[]]]] => 24
[[],[[[]],[],[[[]]]]] => 12
[[],[[[]],[[]],[],[]]] => 48
[[],[[[]],[[]],[[]]]] => 12
[[],[[[]],[[],[]],[]]] => 24
[[],[[[]],[[[]]],[]]] => 12
[[],[[[]],[[],[],[]]]] => 24
[[],[[[]],[[],[[]]]]] => 8
[[],[[[]],[[[]],[]]]] => 8
[[],[[[]],[[[],[]]]]] => 8
[[],[[[]],[[[[]]]]]] => 4
[[],[[[],[]],[],[],[]]] => 96
[[],[[[[]]],[],[],[]]] => 48
[[],[[[],[]],[],[[]]]] => 24
[[],[[[[]]],[],[[]]]] => 12
[[],[[[],[]],[[]],[]]] => 24
[[],[[[[]]],[[]],[]]] => 12
[[],[[[],[]],[[],[]]]] => 16
[[],[[[],[]],[[[]]]]] => 8
[[],[[[[]]],[[],[]]]] => 8
[[],[[[[]]],[[[]]]]] => 4
[[],[[[],[],[]],[],[]]] => 72
[[],[[[],[[]]],[],[]]] => 24
[[],[[[[]],[]],[],[]]] => 24
[[],[[[[],[]]],[],[]]] => 24
[[],[[[[[]]]],[],[]]] => 12
[[],[[[],[],[]],[[]]]] => 24
[[],[[[],[[]]],[[]]]] => 8
[[],[[[[]],[]],[[]]]] => 8
[[],[[[[],[]]],[[]]]] => 8
[[],[[[[[]]]],[[]]]] => 4
[[],[[[],[],[],[]],[]]] => 96
[[],[[[],[],[[]]],[]]] => 24
[[],[[[],[[]],[]],[]]] => 24
[[],[[[],[[],[]]],[]]] => 16
[[],[[[],[[[]]]],[]]] => 8
[[],[[[[]],[],[]],[]]] => 24
[[],[[[[]],[[]]],[]]] => 8
[[],[[[[],[]],[]],[]]] => 16
[[],[[[[[]]],[]],[]]] => 8
[[],[[[[],[],[]]],[]]] => 24
[[],[[[[],[[]]]],[]]] => 8
[[],[[[[[]],[]]],[]]] => 8
[[],[[[[[],[]]]],[]]] => 8
[[],[[[[[[]]]]],[]]] => 4
[[],[[[],[],[],[],[]]]] => 240
[[],[[[],[],[],[[]]]]] => 48
[[],[[[],[],[[]],[]]]] => 48
[[],[[[],[],[[],[]]]]] => 24
[[],[[[],[],[[[]]]]]] => 12
[[],[[[],[[]],[],[]]]] => 48
[[],[[[],[[]],[[]]]]] => 12
[[],[[[],[[],[]],[]]]] => 24
[[],[[[],[[[]]],[]]]] => 12
[[],[[[],[[],[],[]]]]] => 24
[[],[[[],[[],[[]]]]]] => 8
[[],[[[],[[[]],[]]]]] => 8
[[],[[[],[[[],[]]]]]] => 8
[[],[[[],[[[[]]]]]]] => 4
[[],[[[[]],[],[],[]]]] => 48
[[],[[[[]],[],[[]]]]] => 12
[[],[[[[]],[[]],[]]]] => 12
[[],[[[[]],[[],[]]]]] => 8
[[],[[[[]],[[[]]]]]] => 4
[[],[[[[],[]],[],[]]]] => 24
[[],[[[[[]]],[],[]]]] => 12
[[],[[[[],[]],[[]]]]] => 8
[[],[[[[[]]],[[]]]]] => 4
[[],[[[[],[],[]],[]]]] => 24
[[],[[[[],[[]]],[]]]] => 8
[[],[[[[[]],[]],[]]]] => 8
[[],[[[[[],[]]],[]]]] => 8
[[],[[[[[[]]]],[]]]] => 4
[[],[[[[],[],[],[]]]]] => 48
[[],[[[[],[],[[]]]]]] => 12
[[],[[[[],[[]],[]]]]] => 12
[[],[[[[],[[],[]]]]]] => 8
[[],[[[[],[[[]]]]]]] => 4
[[],[[[[[]],[],[]]]]] => 12
[[],[[[[[]],[[]]]]]] => 4
[[],[[[[[],[]],[]]]]] => 8
[[],[[[[[[]]],[]]]]] => 4
[[],[[[[[],[],[]]]]]] => 12
[[],[[[[[],[[]]]]]]] => 4
[[],[[[[[[]],[]]]]]] => 4
[[],[[[[[[],[]]]]]]] => 4
[[],[[[[[[[]]]]]]]] => 2
[[[]],[],[],[],[],[],[]] => 5040
[[[]],[],[],[],[],[[]]] => 720
[[[]],[],[],[],[[]],[]] => 720
[[[]],[],[],[],[[],[]]] => 240
[[[]],[],[],[],[[[]]]] => 120
[[[]],[],[],[[]],[],[]] => 720
[[[]],[],[],[[]],[[]]] => 120
[[[]],[],[],[[],[]],[]] => 240
[[[]],[],[],[[[]]],[]] => 120
[[[]],[],[],[[],[],[]]] => 144
[[[]],[],[],[[],[[]]]] => 48
[[[]],[],[],[[[]],[]]] => 48
[[[]],[],[],[[[],[]]]] => 48
[[[]],[],[],[[[[]]]]] => 24
[[[]],[],[[]],[],[],[]] => 720
[[[]],[],[[]],[],[[]]] => 120
[[[]],[],[[]],[[]],[]] => 120
[[[]],[],[[]],[[],[]]] => 48
[[[]],[],[[]],[[[]]]] => 24
[[[]],[],[[],[]],[],[]] => 240
[[[]],[],[[[]]],[],[]] => 120
[[[]],[],[[],[]],[[]]] => 48
[[[]],[],[[[]]],[[]]] => 24
[[[]],[],[[],[],[]],[]] => 144
[[[]],[],[[],[[]]],[]] => 48
[[[]],[],[[[]],[]],[]] => 48
[[[]],[],[[[],[]]],[]] => 48
[[[]],[],[[[[]]]],[]] => 24
[[[]],[],[[],[],[],[]]] => 144
[[[]],[],[[],[],[[]]]] => 36
[[[]],[],[[],[[]],[]]] => 36
[[[]],[],[[],[[],[]]]] => 24
[[[]],[],[[],[[[]]]]] => 12
[[[]],[],[[[]],[],[]]] => 36
[[[]],[],[[[]],[[]]]] => 12
[[[]],[],[[[],[]],[]]] => 24
[[[]],[],[[[[]]],[]]] => 12
[[[]],[],[[[],[],[]]]] => 36
[[[]],[],[[[],[[]]]]] => 12
[[[]],[],[[[[]],[]]]] => 12
[[[]],[],[[[[],[]]]]] => 12
[[[]],[],[[[[[]]]]]] => 6
[[[]],[[]],[],[],[],[]] => 720
[[[]],[[]],[],[],[[]]] => 120
[[[]],[[]],[],[[]],[]] => 120
[[[]],[[]],[],[[],[]]] => 48
[[[]],[[]],[],[[[]]]] => 24
[[[]],[[]],[[]],[],[]] => 120
[[[]],[[]],[[]],[[]]] => 24
[[[]],[[]],[[],[]],[]] => 48
[[[]],[[]],[[[]]],[]] => 24
[[[]],[[]],[[],[],[]]] => 36
[[[]],[[]],[[],[[]]]] => 12
[[[]],[[]],[[[]],[]]] => 12
[[[]],[[]],[[[],[]]]] => 12
[[[]],[[]],[[[[]]]]] => 6
[[[]],[[],[]],[],[],[]] => 240
[[[]],[[[]]],[],[],[]] => 120
[[[]],[[],[]],[],[[]]] => 48
[[[]],[[[]]],[],[[]]] => 24
[[[]],[[],[]],[[]],[]] => 48
[[[]],[[[]]],[[]],[]] => 24
[[[]],[[],[]],[[],[]]] => 24
[[[]],[[],[]],[[[]]]] => 12
[[[]],[[[]]],[[],[]]] => 12
[[[]],[[[]]],[[[]]]] => 6
[[[]],[[],[],[]],[],[]] => 144
[[[]],[[],[[]]],[],[]] => 48
[[[]],[[[]],[]],[],[]] => 48
[[[]],[[[],[]]],[],[]] => 48
[[[]],[[[[]]]],[],[]] => 24
[[[]],[[],[],[]],[[]]] => 36
[[[]],[[],[[]]],[[]]] => 12
[[[]],[[[]],[]],[[]]] => 12
[[[]],[[[],[]]],[[]]] => 12
[[[]],[[[[]]]],[[]]] => 6
[[[]],[[],[],[],[]],[]] => 144
[[[]],[[],[],[[]]],[]] => 36
[[[]],[[],[[]],[]],[]] => 36
[[[]],[[],[[],[]]],[]] => 24
[[[]],[[],[[[]]]],[]] => 12
[[[]],[[[]],[],[]],[]] => 36
[[[]],[[[]],[[]]],[]] => 12
[[[]],[[[],[]],[]],[]] => 24
[[[]],[[[[]]],[]],[]] => 12
[[[]],[[[],[],[]]],[]] => 36
[[[]],[[[],[[]]]],[]] => 12
[[[]],[[[[]],[]]],[]] => 12
[[[]],[[[[],[]]]],[]] => 12
[[[]],[[[[[]]]]],[]] => 6
[[[]],[[],[],[],[],[]]] => 240
[[[]],[[],[],[],[[]]]] => 48
[[[]],[[],[],[[]],[]]] => 48
[[[]],[[],[],[[],[]]]] => 24
[[[]],[[],[],[[[]]]]] => 12
[[[]],[[],[[]],[],[]]] => 48
[[[]],[[],[[]],[[]]]] => 12
[[[]],[[],[[],[]],[]]] => 24
[[[]],[[],[[[]]],[]]] => 12
[[[]],[[],[[],[],[]]]] => 24
[[[]],[[],[[],[[]]]]] => 8
[[[]],[[],[[[]],[]]]] => 8
[[[]],[[],[[[],[]]]]] => 8
[[[]],[[],[[[[]]]]]] => 4
[[[]],[[[]],[],[],[]]] => 48
[[[]],[[[]],[],[[]]]] => 12
[[[]],[[[]],[[]],[]]] => 12
[[[]],[[[]],[[],[]]]] => 8
[[[]],[[[]],[[[]]]]] => 4
[[[]],[[[],[]],[],[]]] => 24
[[[]],[[[[]]],[],[]]] => 12
[[[]],[[[],[]],[[]]]] => 8
[[[]],[[[[]]],[[]]]] => 4
[[[]],[[[],[],[]],[]]] => 24
[[[]],[[[],[[]]],[]]] => 8
[[[]],[[[[]],[]],[]]] => 8
[[[]],[[[[],[]]],[]]] => 8
[[[]],[[[[[]]]],[]]] => 4
[[[]],[[[],[],[],[]]]] => 48
[[[]],[[[],[],[[]]]]] => 12
[[[]],[[[],[[]],[]]]] => 12
[[[]],[[[],[[],[]]]]] => 8
[[[]],[[[],[[[]]]]]] => 4
[[[]],[[[[]],[],[]]]] => 12
[[[]],[[[[]],[[]]]]] => 4
[[[]],[[[[],[]],[]]]] => 8
[[[]],[[[[[]]],[]]]] => 4
[[[]],[[[[],[],[]]]]] => 12
[[[]],[[[[],[[]]]]]] => 4
[[[]],[[[[[]],[]]]]] => 4
[[[]],[[[[[],[]]]]]] => 4
[[[]],[[[[[[]]]]]]] => 2
[[[],[]],[],[],[],[],[]] => 1440
[[[[]]],[],[],[],[],[]] => 720
[[[],[]],[],[],[],[[]]] => 240
[[[[]]],[],[],[],[[]]] => 120
[[[],[]],[],[],[[]],[]] => 240
[[[[]]],[],[],[[]],[]] => 120
[[[],[]],[],[],[[],[]]] => 96
[[[],[]],[],[],[[[]]]] => 48
[[[[]]],[],[],[[],[]]] => 48
[[[[]]],[],[],[[[]]]] => 24
[[[],[]],[],[[]],[],[]] => 240
[[[[]]],[],[[]],[],[]] => 120
[[[],[]],[],[[]],[[]]] => 48
[[[[]]],[],[[]],[[]]] => 24
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,0,0,0,1 1,6,0,2,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{2} = q$
$F_{3} = q + q^{2}$
$F_{4} = q + 3\ q^{2} + q^{6}$
$F_{5} = q + 6\ q^{2} + 2\ q^{4} + 4\ q^{6} + q^{24}$
$F_{6} = q + 10\ q^{2} + 10\ q^{4} + 10\ q^{6} + 5\ q^{12} + 5\ q^{24} + q^{120}$
$F_{7} = q + 15\ q^{2} + 30\ q^{4} + 20\ q^{6} + 5\ q^{8} + 30\ q^{12} + 15\ q^{24} + 3\ q^{36} + 6\ q^{48} + 6\ q^{120} + q^{720}$
$F_{8} = q + 21\ q^{2} + 70\ q^{4} + 35\ q^{6} + 35\ q^{8} + 105\ q^{12} + 56\ q^{24} + 21\ q^{36} + 42\ q^{48} + 21\ q^{120} + 7\ q^{144} + 7\ q^{240} + 7\ q^{720} + q^{5040}$
Description
The size of the automorphism group of the rooted tree underlying the ordered tree.
Code
def statistic(T):
return factorial(len(T))*prod(statistic(S) for S in T)
Created
Feb 25, 2016 at 21:01 by Martin Rubey
Updated
Feb 25, 2016 at 21:01 by Martin Rubey
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