A229227 The partition function G(n,10).

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213584, 27644267, 190897305, 1382935569, 10479884654, 82861996310, 682044632178, 5832378929502, 51720008131148, 474821737584174, 4506150050048604, 44145239041717738, 445876518513670356

Offset

0,3

Comments

Number G(n,10) of set partitions of {1,...,n} into sets of size at most 10.

Links

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

Formula

E.g.f.: exp(Sum_{j=1..10} 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, 10):
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, 10)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 22 2016

Mathematica

CoefficientList[Exp[Sum[x^j/j!, {j, 1, 10}]] + O[x]^25, x]*Range[0, 24]! (* Jean-François Alcover, May 21 2018 *)

Crossrefs

Column k=10 of A229223.

Cf. A276930.

Sequence in context: A164864 A366776 A192866 * A287589 A287282 A287260

Adjacent sequences: A229224 A229225 A229226 * A229228 A229229 A229230

Keyword

nonn

Author

Alois P. Heinz, Sep 16 2013

Status

approved