%I #32 Jun 07 2023 12:23:03
%S 1,1,3,8,24,71,224,710,2318,7659,25703,87153,298574,1031104,3587263,
%T 12558652,44214807,156438309,555973965,1983817178,7104313970,
%U 25525304569,91986529421,332408847422,1204259931815,4373027942634,15914143511582,58030451159889
%N Number of forests of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
%C Euler transform of A036249 (as well as first differences thereof). - _Franklin T. Adams-Watters_, Feb 08 2006
%H Alois P. Heinz, <a href="/A052855/b052855.txt">Table of n, a(n) for n = 0..1717</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=823">Encyclopedia of Combinatorial Structures 823</a>
%F G.f. satisfies A(x) = exp( Sum_{n>=1} A(x^n)/(1-x^n) * x^n/n ). - _Paul D. Hanna_, Oct 26 2011
%F G.f.: A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{j>=1} Product_{k>=0} (1-x^(j+k))^a(k). - _Seiichi Manyama_, Jun 07 2023
%p spec := [S,{B=Sequence(Z,1 <= card),S=Set(C),C=Prod(B,S)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t max = 26; A[_] = 1; Do[A[x_] = Exp[Sum[A[x^k]/(1 - x^k)*x^k/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[A[x] + O[x]^max, x] (* _Jean-François Alcover_, May 25 2018 *)
%o (PARI) {a(n)=my(A=1+x);for(i=1,n,A=exp(sum(m=1,n,subst(A/(1-x),x,x^m+x*O(x^n))*x^m/m)));polcoeff(A,n)} /* _Paul D. Hanna_, Oct 26 2011 */
%Y First differences of A036249 and A029856.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E More terms from _Franklin T. Adams-Watters_, Feb 08 2006