A327507 - OEIS

%I #8 May 08 2022 08:24:22

%S 1,0,0,0,0,0,1,21,266,2646,22827,179487,1324114,9357348,64991927,

%T 469882413,4008715074,46160063586,691114045987,11535301966755,

%U 194240576089826,3186376950695400,50592286213334943,780299037934036929,11788245937182037114

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

%H Alois P. Heinz, <a href="/A327507/b327507.txt">Table of n, a(n) for n = 0..494</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F E.g.f.: exp((exp(x)-1)^6/6!).

%F a(n) = Sum_{k=0..floor(n/6)} (6*k)! * Stirling2(n,6*k)/(6!^k * k!). - _Seiichi Manyama_, May 07 2022

%p a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)

%p       *binomial(n-1, j-1)*Stirling2(j, 6), j=6..n))

%p     end:

%p seq(a(n), n=0..27);

%o (PARI) a(n) = sum(k=0, n\6, (6*k)!*stirling(n, 6*k, 2)/(6!^k*k!)); \\ _Seiichi Manyama_, May 07 2022

%Y Column k=6 of A324162.

%K nonn

%O 0,8

%A _Alois P. Heinz_, Sep 14 2019