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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.

%I A275099 #12 Jun 27 2022 07:54:40
%S A275099 1,1,513,10136746,2672797504001,5260857687009765626,
%T A275099 53531132944198868710856802,2185249026716732313958375321948613,
%U A275099 297263694975439941710846391262298377605633,116941828532092016226313310933885429108622288425362
%N 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.
%H A275099 Alois P. Heinz, <a href="/A275099/b275099.txt">Table of n, a(n) for n = 0..75</a>
%H A275099 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 A275099 Sum_{n>=0} a(n) * x^n / (n!)^10 = exp(Sum_{n>=1} x^n / (n!)^10). - _Ilya Gutkovskiy_, Jul 17 2020
%p A275099 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A275099       binomial(n, j)^10*(n-j)*a(j), j=0..n-1)/n)
%p A275099     end:
%p A275099 seq(a(n), n=0..12);
%t A275099 a[n_] := a[n] = If[n==0, 1, Sum[Binomial[n, j]^10*(n-j)*a[j], {j, 0, n-1}]/n];
%t A275099 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Jun 27 2022, after _Alois P. Heinz_ *)
%Y A275099 Column k=10 of A275043.
%K A275099 nonn
%O A275099 0,3
%A A275099 _Alois P. Heinz_, Jul 16 2016