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A327508 Number of set partitions of [n] where each subset is again partitioned into seven nonempty subsets.

%I A327508 #8 May 08 2022 08:24:18
%S A327508 1,0,0,0,0,0,0,1,28,462,5880,63987,627396,5715424,49330996,408921513,
%T A327508 3292212924,26136933186,211891946448,1910903676319,21958686224932,
%U A327508 338516695449108,6257281367040396,122152192372692405,2369188918134769500,44783158458575933110
%N A327508 Number of set partitions of [n] where each subset is again partitioned into seven nonempty subsets.
%H A327508 Alois P. Heinz, <a href="/A327508/b327508.txt">Table of n, a(n) for n = 0..496</a>
%H A327508 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A327508 E.g.f.: exp((exp(x)-1)^7/7!).
%F A327508 a(n) = Sum_{k=0..floor(n/7)} (7*k)! * Stirling2(n,7*k)/(7!^k * k!). - _Seiichi Manyama_, May 07 2022
%p A327508 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
%p A327508       *binomial(n-1, j-1)*Stirling2(j, 7), j=7..n))
%p A327508     end:
%p A327508 seq(a(n), n=0..27);
%o A327508 (PARI) a(n) = sum(k=0, n\7, (7*k)!*stirling(n, 7*k, 2)/(7!^k*k!)); \\ _Seiichi Manyama_, May 07 2022
%Y A327508 Column k=7 of A324162.
%K A327508 nonn
%O A327508 0,9
%A A327508 _Alois P. Heinz_, Sep 14 2019