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A327511 Number of set partitions of [n] where each subset is again partitioned into ten nonempty subsets.

%I A327511 #8 May 08 2022 08:24:06
%S A327511 1,0,0,0,0,0,0,0,0,0,1,55,1705,39325,752752,12662650,193754990,
%T A327511 2758334150,37112163803,477297033785,5917585057033,71187151690655,
%U A327511 835145968875284,9593573078823360,108264887496309962,1203738001326003000,13226402531839795155
%N A327511 Number of set partitions of [n] where each subset is again partitioned into ten nonempty subsets.
%H A327511 Alois P. Heinz, <a href="/A327511/b327511.txt">Table of n, a(n) for n = 0..502</a>
%H A327511 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A327511 E.g.f.: exp((exp(x)-1)^10/10!).
%F A327511 a(n) = Sum_{k=0..floor(n/10)} (10*k)! * Stirling2(n,10*k)/(10!^k * k!). - _Seiichi Manyama_, May 07 2022
%p A327511 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
%p A327511       *binomial(n-1, j-1)*Stirling2(j, 10), j=10..n))
%p A327511     end:
%p A327511 seq(a(n), n=0..27);
%o A327511 (PARI) a(n) = sum(k=0, n\10, (10*k)!*stirling(n, 10*k, 2)/(10!^k*k!)); \\ _Seiichi Manyama_, May 07 2022
%Y A327511 Column k=10 of A324162.
%K A327511 nonn
%O A327511 0,12
%A A327511 _Alois P. Heinz_, Sep 14 2019