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A327509 Number of set partitions of [n] where each subset is again partitioned into eight nonempty subsets.

%I A327509 #8 May 08 2022 08:24:14
%S A327509 1,0,0,0,0,0,0,0,1,36,750,11880,159027,1899612,20912320,216627840,
%T A327509 2141770488,20416870188,189100389270,1713143123640,15314761051669,
%U A327509 137723007972924,1310008783707360,14647748873844240,215375952901752225,4079250159907459680
%N A327509 Number of set partitions of [n] where each subset is again partitioned into eight nonempty subsets.
%H A327509 Alois P. Heinz, <a href="/A327509/b327509.txt">Table of n, a(n) for n = 0..498</a>
%H A327509 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A327509 E.g.f.: exp((exp(x)-1)^8/8!).
%F A327509 a(n) = Sum_{k=0..floor(n/8)} (8*k)! * Stirling2(n,8*k)/(8!^k * k!). - _Seiichi Manyama_, May 07 2022
%p A327509 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
%p A327509       *binomial(n-1, j-1)*Stirling2(j, 8), j=8..n))
%p A327509     end:
%p A327509 seq(a(n), n=0..27);
%o A327509 (PARI) a(n) = sum(k=0, n\8, (8*k)!*stirling(n, 8*k, 2)/(8!^k*k!)); \\ _Seiichi Manyama_, May 07 2022
%Y A327509 Column k=8 of A324162.
%K A327509 nonn
%O A327509 0,10
%A A327509 _Alois P. Heinz_, Sep 14 2019