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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.
2
1, 1, 257, 1699300, 112660505345, 44687884101953126, 76502602935955053437072, 451167428778794282789329512425, 7771744024861563765933540267436016385, 344735749788852590196707169431958672823413322, 35650419033178479865362827431736721104304210986866382
OFFSET
0,3
LINKS
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.
FORMULA
Sum_{n>=0} a(n) * x^n / (n!)^9 = exp(Sum_{n>=1} x^n / (n!)^9). - Ilya Gutkovskiy, Jul 17 2020
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);
CROSSREFS
Column k=9 of A275043.
Sequence in context: A283510 A103349 A291506 * A194155 A238614 A308672
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 16 2016
STATUS
approved