A276925 Number of ordered set partitions of [n] with at most five elements per block.

1, 1, 3, 13, 75, 541, 4682, 47278, 545594, 7083258, 102177222, 1621316466, 28065324210, 526301293518, 10628781887724, 229983021824556, 5308071700475544, 130168746864660504, 3379871981604782664, 92634950510491052664, 2672550322299614660904

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=5 of A276921.

Cf. A110038.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
       a(n-i)*binomial(n, i), i=1..min(n, 5)))
    end:
seq(a(n), n=0..25);

Mathematica

max = 25; CoefficientList[1/(1-Sum[x^i/i!, {i, 1, 5}]) + O[x]^(max+1), x]* Range[0, max]! (* Jean-François Alcover, May 24 2018 *)

Formula

E.g.f.: 1/(1-Sum_{i=1..5} x^i/i!).