A032311 Number of ways to partition n labeled elements into sets of different sizes of at least 2.

1, 0, 1, 1, 1, 11, 16, 57, 85, 1507, 2896, 12563, 51074, 138789, 2954407, 7959304, 38908797, 178913747, 1100724688, 3444477663, 114462103390, 358862880667, 2217915340389, 11257750157888, 73465378482214, 515469706792741, 2247201695123581, 98470393431973852

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..698
• C. G. Bower, Transforms (2)

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`(i<2, 0, b(n, i-1)+
      `if`(i>n, 0, b(n-i, i-1)*binomial(n, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, May 11 2016

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 2, 0, b[n, i - 1] + If[i > n, 0, b[n - i, i - 1]*Binomial[n, i]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 27 2017, after Alois P. Heinz *)

PARI

seq(n)={Vec(serlaplace(prod(k=2, n, 1 + x^k/k! + O(x*x^n))))} \\ Andrew Howroyd, Sep 11 2018

Formula

"EGJ" (unordered, element, labeled) transform of 0, 1, 1, 1...

E.g.f: Product_{k >= 2} (1 + x^k/k!). - Andrew Howroyd, Sep 11 2018

Extensions

a(0)=1 prepended by Alois P. Heinz, May 11 2016