A275424 Number of set partitions of [n] such that six is a multiple of each block size.

1, 1, 2, 5, 14, 46, 167, 659, 2836, 13064, 64076, 333928, 1834438, 10592518, 64136528, 405519766, 2672202304, 18315499424, 130245129112, 959527765480, 7311915167696, 57536223460640, 466963917417152, 3904133599120624, 33583586584746728, 296948602314737576

Offset: 0

Author

Alois P. Heinz, Jul 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..603
• Wikipedia, Partition of a set

Crossrefs

Column k=6 of A275422.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 2, 3, 6]))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 2, 3, 6}}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Formula

E.g.f.: exp(x+x^2/2+x^3/6+x^6/6!).