A276924 Number of ordered set partitions of [n] with at most four elements per block.

1, 1, 3, 13, 75, 540, 4670, 47110, 543130, 7044450, 101519250, 1609319250, 27830729850, 521397676800, 10519576867800, 227400111939000, 5243385642495000, 128458209887007000, 3332234177825553000, 91241046790816923000, 2629791992312269785000

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=4 of A276921.

Cf. A001681.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
       a(n-i)*binomial(n, i), i=1..min(n, 4)))
    end:
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*(<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1/24|1/6|1/2|1>>^n)[4, 4]:
seq(a(n), n=0..25);

Mathematica

max = 20; CoefficientList[1/(1-Sum[x^i/i!, {i, 1, 4}]) + O[x]^(max+1), x]* Range[0, max]! (* Jean-François Alcover, May 24 2018 *)

Formula

E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!).