A229225 The partition function G(n,8).

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115964, 678448, 4212352, 27632112, 190778186, 1381763398, 10468226150, 82744297014, 680835331228, 5819712427654, 51584619782546, 473344099095848, 4489677962922186, 43957668431564086, 443694809361207824

Offset: 0

Author

Alois P. Heinz, Sep 16 2013

Keywords

• nonn

Comments

Number G(n,8) of set partitions of {1,...,n} into sets of size at most 8.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Column k=8 of A229223.

Cf. A276928.

Programs

Maple

G:= proc(n, k) option remember; local j; if k>n then G(n, n)
      elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
      for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
    end:
a:= n-> G(n, 8):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
       a(n-i)*binomial(n-1, i-1), i=1..min(n, 8)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 22 2016

Mathematica

CoefficientList[Exp[Sum[x^j/j!, {j, 1, 8}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)

Formula

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