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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..603

Wikipedia, Partition of a set

Formula

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

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 *)

Crossrefs

Column k=6 of A275422.

Sequence in context: A240616 A240617 A001680 * A328429 A107268 A231211

Adjacent sequences: A275421 A275422 A275423 * A275425 A275426 A275427

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2016

Status

approved