A275099 Number of set partitions of [10*n] such that within each block the numbers of elements from all residue classes modulo 10 are equal.

1, 1, 513, 10136746, 2672797504001, 5260857687009765626, 53531132944198868710856802, 2185249026716732313958375321948613, 297263694975439941710846391262298377605633, 116941828532092016226313310933885429108622288425362

Offset: 0

Author

Alois P. Heinz, Jul 16 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..75
• J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Crossrefs

Column k=10 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n, j)^10*(n-j)*a(j), j=0..n-1)/n)
    end:
seq(a(n), n=0..12);

Mathematica

a[n_] := a[n] = If[n==0, 1, Sum[Binomial[n, j]^10*(n-j)*a[j], {j, 0, n-1}]/n];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jun 27 2022, after Alois P. Heinz *)

Formula

Sum_{n>=0} a(n) * x^n / (n!)^10 = exp(Sum_{n>=1} x^n / (n!)^10). - Ilya Gutkovskiy, Jul 17 2020