A275098 Number of set partitions of [9*n] such that within each block the numbers of elements from all residue classes modulo 9 are equal.

1, 1, 257, 1699300, 112660505345, 44687884101953126, 76502602935955053437072, 451167428778794282789329512425, 7771744024861563765933540267436016385, 344735749788852590196707169431958672823413322, 35650419033178479865362827431736721104304210986866382

Offset: 0

Author

Alois P. Heinz, Jul 16 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..82
• 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=9 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n, j)^9*(n-j)*a(j), j=0..n-1)/n)
    end:
seq(a(n), n=0..12);

Formula

Sum_{n>=0} a(n) * x^n / (n!)^9 = exp(Sum_{n>=1} x^n / (n!)^9). - Ilya Gutkovskiy, Jul 17 2020