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A275097 Number of set partitions of [8*n] such that within each block the numbers of elements from all residue classes modulo 8 are equal.

%I A275097 #8 Jul 17 2020 10:25:31
%S A275097 1,1,129,286498,4802367617,386652630390626,112344305783644570242,
%T A275097 96703375432646667737903621,213426677887357366350726096998529,
%U A275097 1081530653290057746718498987187644516546,11534313393388449518393789691807687515711518754
%N A275097 Number of set partitions of [8*n] such that within each block the numbers of elements from all residue classes modulo 8 are equal.
%H A275097 Alois P. Heinz, <a href="/A275097/b275097.txt">Table of n, a(n) for n = 0..91</a>
%H A275097 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 A275097 Sum_{n>=0} a(n) * x^n / (n!)^8 = exp(Sum_{n>=1} x^n / (n!)^8). - _Ilya Gutkovskiy_, Jul 17 2020
%p A275097 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275097       binomial(n, j)^8*(n-j)*a(j), j=0..n-1)/n)
%p A275097     end:
%p A275097 seq(a(n), n=0..12);
%Y A275097 Column k=8 of A275043.
%K A275097 nonn
%O A275097 0,3
%A A275097 _Alois P. Heinz_, Jul 16 2016