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

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..495

Wikipedia, Partition of a set

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

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 *)

Prog

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

Crossrefs

Column k=4 of A324162.

Cf. A346895.

Sequence in context: A000453 A365532 A365525 * A346954 A346895 A291231

Adjacent sequences: A327502 A327503 A327504 * A327506 A327507 A327508

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved