Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001608
Mapping
St001608: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 2
[3]
 => 2
[2,1]
 => 5
[1,1,1]
 => 9
[4]
 => 4
[3,1]
 => 13
[2,2]
 => 18
[2,1,1]
 => 34
[1,1,1,1]
 => 64
[5]
 => 9
[4,1]
 => 35
[3,2]
 => 63
[3,1,1]
 => 119
[2,2,1]
 => 171
[2,1,1,1]
 => 326
[1,1,1,1,1]
 => 625
[6]
 => 20
[5,1]
 => 95
[4,2]
 => 209
[4,1,1]
 => 401
[3,3]
 => 268
[3,2,1]
 => 744
[3,1,1,1]
 => 1433
[2,2,2]
 => 1077
[2,2,1,1]
 => 2078
[2,1,1,1,1]
 => 4016
[1,1,1,1,1,1]
 => 7776
[7]
 => 48
[6,1]
 => 262
[5,2]
 => 683
[5,1,1]
 => 1316
[4,3]
 => 1065
[4,2,1]
 => 2993
[4,1,1,1]
 => 5799
[3,3,1]
 => 3868
[3,2,2]
 => 5637
[3,2,1,1]
 => 10937
[3,1,1,1,1]
 => 21256
[2,2,2,1]
 => 15955
[2,2,1,1,1]
 => 31022
[2,1,1,1,1,1]
 => 60387
[1,1,1,1,1,1,1]
 => 117649
[8]
 => 115
[7,1]
 => 727
[6,2]
 => 2189
[6,1,1]
 => 4247
[5,3]
 => 4022
[5,2,1]
 => 11417
Description
The number of coloured rooted 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 rooted trees on $n$ vertices, [[oeis:A000081]], whereas the value on the partition $(1^n)$ is the number of labelled rooted trees [[oeis:A000169]].