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A032311 Number of ways to partition n labeled elements into sets of different sizes of at least 2. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)