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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Wikipedia, Partition of a set

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 *)

Crossrefs

Row sums of A324162.

Sequence in context: A183425 A039628 A194530 * A005964 A246138 A129416

Adjacent sequences: A324235 A324236 A324237 * A324239 A324240 A324241

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2019

Status

approved