A275428 Number of set partitions of [n] such that ten is a multiple of each block size.

1, 1, 2, 4, 10, 27, 82, 274, 988, 3880, 16175, 72205, 340660, 1697060, 8906990, 48911059, 281486144, 1687198848, 10535484376, 68349098640, 459596780618, 3202506672898, 23052054364956, 171418420964352, 1314125642973640, 10375794542251692, 84315714183790792

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..607

Wikipedia, Partition of a set

Formula

E.g.f.: exp(x+x^2/2+x^5/5!+x^10/10!).

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, 5, 10]))
    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, 5, 10}}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=10 of A275422.

Sequence in context: A121690 A138356 A287693 * A202058 A346999 A148107

Adjacent sequences: A275425 A275426 A275427 * A275429 A275430 A275431

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2016

Status

approved