A275427 Number of set partitions of [n] such that nine is a multiple of each block size.

1, 1, 1, 2, 5, 11, 31, 106, 337, 1206, 5031, 20241, 86901, 421422, 2014377, 10015461, 54946881, 301009311, 1692429867, 10319449158, 63321896601, 395830490301, 2648669976261, 17920165424382, 122976000215289, 894420751179276, 6596034524038701, 49207275464475051

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..617

Wikipedia, Partition of a set

Formula

E.g.f.: exp(x+x^3/6+x^9/9!).

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, 3, 9]))
    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, 3, 9}}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=9 of A275422.

Sequence in context: A124481 A002862 A190865 * A139464 A174537 A101837

Adjacent sequences: A275424 A275425 A275426 * A275428 A275429 A275430

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2016

Status

approved