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

1, 1, 3, 9, 32, 133, 625, 3328, 20172, 137073, 1023610, 8327069, 73711863, 707141074, 7278630390, 79522233635, 916354807657, 11119419230485, 142082222254701, 1908850117706652, 26862951637197372, 394233330125117457, 6013602782397882264, 95208871146458467659

Offset: 0

Author

Alois P. Heinz, Sep 02 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Wikipedia, Partition of a set

Crossrefs

Row sums of A324162.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0 or k>n, 0,
      add(b(n-j, k)*binomial(n-1, j-1)*Stirling2(j, k), j=k..n)))
    end:
a:= n-> add(b(n, k), k=0..n):
seq(a(n), n=0..23);

Mathematica

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}]]];
a[n_] := Sum[b[n, k], {k, 0, n}];
a /@ Range[0, 23] (* Jean-François Alcover, May 05 2020, after Maple *)