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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Column k=4 of A276921.

Cf. A001681.

Sequence in context: A334637 A007178 A173990 * A343788 A276895 A276925

Adjacent sequences: A276921 A276922 A276923 * A276925 A276926 A276927

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2016

Status

approved