Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001609
Mapping
St001609: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 2
[1,1,1]
 => 3
[4]
 => 2
[3,1]
 => 4
[2,2]
 => 6
[2,1,1]
 => 9
[1,1,1,1]
 => 16
[5]
 => 3
[4,1]
 => 9
[3,2]
 => 15
[3,1,1]
 => 26
[2,2,1]
 => 37
[2,1,1,1]
 => 67
[1,1,1,1,1]
 => 125
[6]
 => 6
[5,1]
 => 20
[4,2]
 => 43
[4,1,1]
 => 75
[3,3]
 => 51
[3,2,1]
 => 134
[3,1,1,1]
 => 251
[2,2,2]
 => 195
[2,2,1,1]
 => 359
[2,1,1,1,1]
 => 680
[1,1,1,1,1,1]
 => 1296
[7]
 => 11
[6,1]
 => 48
[5,2]
 => 116
[5,1,1]
 => 214
[4,3]
 => 175
[4,2,1]
 => 469
[4,1,1,1]
 => 888
[3,3,1]
 => 596
[3,2,2]
 => 861
[3,2,1,1]
 => 1636
[3,1,1,1,1]
 => 3135
[2,2,2,1]
 => 2365
[2,2,1,1,1]
 => 4530
[2,1,1,1,1,1]
 => 8716
[1,1,1,1,1,1,1]
 => 16807
[8]
 => 23
[7,1]
 => 115
[6,2]
 => 329
[6,1,1]
 => 612
[5,3]
 => 573
[5,2,1]
 => 1577
Description
The number of coloured trees such that the multiplicities of colours are given by a partition. In particular, the value on the partition $(n)$ is the number of unlabelled trees on $n$ vertices, [[oeis:A000055]], whereas the value on the partition $(1^n)$ is the number of labelled trees [[oeis:A000272]].