A327505 Number of set partitions of [n] where each subset is again partitioned into four nonempty subsets.

1, 0, 0, 0, 1, 10, 65, 350, 1736, 9030, 60355, 561550, 6183221, 69469400, 761767370, 8239194600, 91058524831, 1073790441370, 13900626022985, 196759304278250, 2963381404815566, 46227649788125190, 736940002561065325, 12005645243802471250, 201482801573414254301

Offset: 0

Author

Alois P. Heinz, Sep 14 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..495
• Wikipedia, Partition of a set

Crossrefs

Column k=4 of A324162.

Cf. A346895.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
      *binomial(n-1, j-1)*Stirling2(j, 4), j=4..n))
    end:
seq(a(n), n=0..25);

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[a[n - j] Binomial[n - 1, j - 1] StirlingS2[j, 4], {j, 4, n}]];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)

PARI

a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 2)/(24^k*k!)); \\ Seiichi Manyama, May 07 2022

Formula

E.g.f.: exp((exp(x)-1)^4/4!).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling2(n,4*k)/(24^k * k!). - Seiichi Manyama, May 07 2022