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

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..698

C. G. Bower, Transforms (2)

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

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 *)

Prog

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

Crossrefs

Sequence in context: A316171 A184064 A302207 * A032221 A032146 A032051

Adjacent sequences: A032308 A032309 A032310 * A032312 A032313 A032314

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved