A327510 - OEIS

%I #8 May 08 2022 08:24:09

%S 1,0,0,0,0,0,0,0,0,1,45,1155,22275,359502,5135130,67128490,820784250,

%T 9528822303,106175420065,1144618783815,12011663703975,123297356170054,

%U 1243260840764910,12377559175117290,122870882863640450,1247553197735599755,13803307806688911225

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

%H Alois P. Heinz, <a href="/A327510/b327510.txt">Table of n, a(n) for n = 0..500</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)^9/9!).

%F a(n) = Sum_{k=0..floor(n/9)} (9*k)! * Stirling2(n,9*k)/(9!^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, 9), j=9..n))

%p     end:

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

%o (PARI) a(n) = sum(k=0, n\9, (9*k)!*stirling(n, 9*k, 2)/(9!^k*k!)); \\ _Seiichi Manyama_, May 07 2022

%Y Column k=9 of A324162.

%K nonn

%O 0,11

%A _Alois P. Heinz_, Sep 14 2019