A229226 The partition function G(n,9).

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678558, 4213452, 27642837, 190882290, 1382779413, 10478259030, 82844940414, 681863474058, 5830425411936, 51698581146426, 474582397380708, 4503425395487976, 44113612993755306, 445502134752984696

Offset

0,3

Comments

Number G(n,9) of set partitions of {1,...,n} into sets of size at most 9.

Links

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

Formula

E.g.f.: exp(Sum_{j=1..9} x^j/j!).

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, 9):
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, 9)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 22 2016

Mathematica

CoefficientList[Exp[Sum[x^j/j!, {j, 1, 9}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)

Crossrefs

Column k=9 of A229223.

Cf. A276929.

Sequence in context: A287670 A164863 A192126 * A343671 A276726 A287588

Adjacent sequences: A229223 A229224 A229225 * A229227 A229228 A229229

Keyword

nonn

Author

Alois P. Heinz, Sep 16 2013

Status

approved