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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.

%I A275098 #7 Jul 17 2020 10:24:52
%S A275098 1,1,257,1699300,112660505345,44687884101953126,
%T A275098 76502602935955053437072,451167428778794282789329512425,
%U A275098 7771744024861563765933540267436016385,344735749788852590196707169431958672823413322,35650419033178479865362827431736721104304210986866382
%N 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.
%H A275098 Alois P. Heinz, <a href="/A275098/b275098.txt">Table of n, a(n) for n = 0..82</a>
%H A275098 J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
%F A275098 Sum_{n>=0} a(n) * x^n / (n!)^9 = exp(Sum_{n>=1} x^n / (n!)^9). - _Ilya Gutkovskiy_, Jul 17 2020
%p A275098 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275098       binomial(n, j)^9*(n-j)*a(j), j=0..n-1)/n)
%p A275098     end:
%p A275098 seq(a(n), n=0..12);
%Y A275098 Column k=9 of A275043.
%K A275098 nonn
%O A275098 0,3
%A A275098 _Alois P. Heinz_, Jul 16 2016