A275426 Number of set partitions of [n] such that eight is a multiple of each block size.

1, 1, 2, 4, 11, 31, 106, 372, 1500, 6220, 28696, 136016, 702802, 3727946, 21253324, 124231096, 772458366, 4918962462, 33061094812, 227303566648, 1639389311906, 12082068225466, 92951836390172, 729991698024568, 5960615982017512, 49636995406898376

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..604

Wikipedia, Partition of a set

Formula

E.g.f.: exp(x+x^2/2+x^4/24+x^8/8!).

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, 4, 8]))
    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, 4, 8}}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=8 of A275422.

Sequence in context: A148169 A110140 A190452 * A115625 A056323 A081557

Adjacent sequences: A275423 A275424 A275425 * A275427 A275428 A275429

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2016

Status

approved