A327506 Number of set partitions of [n] where each subset is again partitioned into five nonempty subsets.

1, 0, 0, 0, 0, 1, 15, 140, 1050, 6951, 42651, 253660, 1594230, 12463451, 134921787, 1806386946, 25524454410, 354189159871, 4751404201923, 62042283083648, 803415873180606, 10624141898153091, 148849893975447819, 2279247411153872566, 38395707003954897234

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..494

Wikipedia, Partition of a set

Formula

E.g.f.: exp((exp(x)-1)^5/5!).

a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k)/(120^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, 5), j=5..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, 5], {j, 5, n}]];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)

Prog

(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2)/(120^k*k!)); \\ Seiichi Manyama, May 07 2022

Crossrefs

Column k=5 of A324162.

Sequence in context: A056281 A000481 A365528 * A346955 A346920 A215765

Adjacent sequences: A327503 A327504 A327505 * A327507 A327508 A327509

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved