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A324238 Number of set partitions of [n] where all subsets are partitioned into the same number of nonempty subsets.

%I A324238 #25 May 05 2020 04:28:44
%S A324238 1,1,3,9,32,133,625,3328,20172,137073,1023610,8327069,73711863,
%T A324238 707141074,7278630390,79522233635,916354807657,11119419230485,
%U A324238 142082222254701,1908850117706652,26862951637197372,394233330125117457,6013602782397882264,95208871146458467659
%N A324238 Number of set partitions of [n] where all subsets are partitioned into the same number of nonempty subsets.
%H A324238 Alois P. Heinz, <a href="/A324238/b324238.txt">Table of n, a(n) for n = 0..300</a>
%H A324238 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A324238 b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0 or k>n, 0,
%p A324238       add(b(n-j, k)*binomial(n-1, j-1)*Stirling2(j, k), j=k..n)))
%p A324238     end:
%p A324238 a:= n-> add(b(n, k), k=0..n):
%p A324238 seq(a(n), n=0..23);
%t A324238 b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n-j, k]* Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];
%t A324238 a[n_] := Sum[b[n, k], {k, 0, n}];
%t A324238 a /@ Range[0, 23] (* _Jean-François Alcover_, May 05 2020, after Maple *)
%Y A324238 Row sums of A324162.
%K A324238 nonn
%O A324238 0,3
%A A324238 _Alois P. Heinz_, Sep 02 2019