cp's OEIS Frontend

A327507 Number of set partitions of [n] where each subset is again partitioned into six nonempty subsets.

%I A327507 #8 May 08 2022 08:24:22
%S A327507 1,0,0,0,0,0,1,21,266,2646,22827,179487,1324114,9357348,64991927,
%T A327507 469882413,4008715074,46160063586,691114045987,11535301966755,
%U A327507 194240576089826,3186376950695400,50592286213334943,780299037934036929,11788245937182037114
%N A327507 Number of set partitions of [n] where each subset is again partitioned into six nonempty subsets.
%H A327507 Alois P. Heinz, <a href="/A327507/b327507.txt">Table of n, a(n) for n = 0..494</a>
%H A327507 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A327507 E.g.f.: exp((exp(x)-1)^6/6!).
%F A327507 a(n) = Sum_{k=0..floor(n/6)} (6*k)! * Stirling2(n,6*k)/(6!^k * k!). - _Seiichi Manyama_, May 07 2022
%p A327507 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
%p A327507       *binomial(n-1, j-1)*Stirling2(j, 6), j=6..n))
%p A327507     end:
%p A327507 seq(a(n), n=0..27);
%o A327507 (PARI) a(n) = sum(k=0, n\6, (6*k)!*stirling(n, 6*k, 2)/(6!^k*k!)); \\ _Seiichi Manyama_, May 07 2022
%Y A327507 Column k=6 of A324162.
%K A327507 nonn
%O A327507 0,8
%A A327507 _Alois P. Heinz_, Sep 14 2019