A327504 Number of set partitions of [n] where each subset is again partitioned into three nonempty subsets.

1, 0, 0, 1, 6, 25, 100, 511, 3626, 29765, 250200, 2146771, 19575446, 195336505, 2124840900, 24646324431, 299803782466, 3809251939245, 50698296967600, 708349718638891, 10372758309704686, 158546862369781985, 2519789706502636700, 41545703617137280551

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..501

Wikipedia, Partition of a set

Formula

E.g.f.: exp((exp(x)-1)^3/3!).

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/(6^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, 3), j=3..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, 3], {j, 3, n}]];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/(6^k*k!)); \\ Seiichi Manyama, May 07 2022

Crossrefs

Column k=3 of A324162.

Cf. A346894.

Sequence in context: A034559 A034347 A009121 * A346390 A323824 A037537

Adjacent sequences: A327501 A327502 A327503 * A327505 A327506 A327507

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved