A276928 Number of ordered set partitions of [n] with at most eight elements per block.

1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087260, 102247542, 1622632110, 28091557362, 526858114926, 10641337416138, 230283052622766, 5315651069181882, 130370668142722722, 3385531828379161890, 92801502294634265418, 2677685131818279016434

Offset: 0

Author

Alois P. Heinz, Sep 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..424

Crossrefs

Column k=8 of A276921.

Cf. A229225.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
       a(n-i)*binomial(n, i), i=1..min(n, 8)))
    end:
seq(a(n), n=0..25);

Mathematica

max = 25; CoefficientList[1/(1-Sum[x^i/i!, {i, 1, 8}]) + O[x]^(max+1), x]* Range[0, max]! (* Jean-François Alcover, May 24 2018 *)

Formula

E.g.f.: 1/(1-Sum_{i=1..8} x^i/i!).