Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001561
Mapping
St001561: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 0
[1,1]
 => 4
[3]
 => 0
[2,1]
 => 2
[1,1,1]
 => 27
[4]
 => 0
[3,1]
 => 0
[2,2]
 => 1
[2,1,1]
 => 27
[1,1,1,1]
 => 256
[5]
 => 0
[4,1]
 => 0
[3,2]
 => 0
[3,1,1]
 => 9
[2,2,1]
 => 27
[2,1,1,1]
 => 384
[1,1,1,1,1]
 => 3125
[6]
 => 0
[5,1]
 => 0
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 0
[3,2,1]
 => 9
[3,1,1,1]
 => 256
[2,2,2]
 => 27
[2,2,1,1]
 => 576
[2,1,1,1,1]
 => 6250
[1,1,1,1,1,1]
 => 46656
[7]
 => 0
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 0
[4,3]
 => 0
[4,2,1]
 => 0
[4,1,1,1]
 => 64
[3,3,1]
 => 3
[3,2,2]
 => 9
[3,2,1,1]
 => 384
[3,1,1,1,1]
 => 6250
[2,2,2,1]
 => 864
[2,2,1,1,1]
 => 12500
[2,1,1,1,1,1]
 => 116640
[1,1,1,1,1,1,1]
 => 823543
[8]
 => 0
[7,1]
 => 0
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 0
[5,2,1]
 => 0
Description
The value of the elementary symmetric function evaluated at 1. The statistic is $e_\lambda(x_1,\dotsc,x_k)$ evaluated at $x_1=x_2=\dotsb=x_k=1$, where $\lambda$ has $k$ parts. Thus, the statistic is equal to $\prod_{j=1}^k \frac{(k)_{\lambda_j}}{\lambda_j!}$ where $\lambda$ has $k$ parts.