Processing math: 100%

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Matching statistic: St001611
Mapping
St001611: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 3
[2,1]
 => 4
[1,1,1]
 => 5
[4]
 => 5
[3,1]
 => 7
[2,2]
 => 9
[2,1,1]
 => 11
[1,1,1,1]
 => 15
[5]
 => 7
[4,1]
 => 12
[3,2]
 => 16
[3,1,1]
 => 21
[2,2,1]
 => 26
[2,1,1,1]
 => 36
[1,1,1,1,1]
 => 52
[6]
 => 11
[5,1]
 => 19
[4,2]
 => 29
[4,1,1]
 => 38
[3,3]
 => 31
[3,2,1]
 => 52
[3,1,1,1]
 => 74
[2,2,2]
 => 66
[2,2,1,1]
 => 92
[2,1,1,1,1]
 => 135
[1,1,1,1,1,1]
 => 203
[7]
 => 15
[6,1]
 => 30
[5,2]
 => 47
[5,1,1]
 => 64
[4,3]
 => 57
[4,2,1]
 => 98
[4,1,1,1]
 => 141
[3,3,1]
 => 109
[3,2,2]
 => 137
[3,2,1,1]
 => 198
[3,1,1,1,1]
 => 296
[2,2,2,1]
 => 249
[2,2,1,1,1]
 => 371
[2,1,1,1,1,1]
 => 566
[1,1,1,1,1,1,1]
 => 877
[8]
 => 22
[7,1]
 => 45
[6,2]
 => 77
[6,1,1]
 => 105
[5,3]
 => 97
[5,2,1]
 => 171
Description
The number of multiset partitions such that the multiplicities of elements are given by a partition. In particular, the value on the partition (n) is the number of integer partitions of n, [[oeis:A000041]], whereas the value on the partition (1n) is the number of set partitions [[oeis:A006110]].