%I #18 Sep 11 2018 16:01:10
%S 1,0,1,1,1,11,16,57,85,1507,2896,12563,51074,138789,2954407,7959304,
%T 38908797,178913747,1100724688,3444477663,114462103390,358862880667,
%U 2217915340389,11257750157888,73465378482214,515469706792741,2247201695123581,98470393431973852
%N Number of ways to partition n labeled elements into sets of different sizes of at least 2.
%H Alois P. Heinz, <a href="/A032311/b032311.txt">Table of n, a(n) for n = 0..698</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%F "EGJ" (unordered, element, labeled) transform of 0, 1, 1, 1...
%F E.g.f: Product_{k >= 2} (1 + x^k/k!). - _Andrew Howroyd_, Sep 11 2018
%p b:= proc(n, i) option remember;
%p `if`(n=0, 1, `if`(i<2, 0, b(n, i-1)+
%p `if`(i>n, 0, b(n-i, i-1)*binomial(n, i))))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, May 11 2016
%t 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_ *)
%o (PARI) seq(n)={Vec(serlaplace(prod(k=2, n, 1 + x^k/k! + O(x*x^n))))} \\ _Andrew Howroyd_, Sep 11 2018
%K nonn
%O 0,6
%A _Christian G. Bower_
%E a(0)=1 prepended by _Alois P. Heinz_, May 11 2016