%I
%S 1,1,1,6,28,235,2466,31864,488328,8901981,183417490,4300791946,
%T 111621409956,3214239089659,100662133475372,3440691046061130,
%U 126342964714732576,4999000389915029881,210671936366279249610,9474491260037610708598,450638933972015166026220
%N Number of forests of trees on n labeled nodes in which each tree has a distinct number of vertices.
%H Alois P. Heinz, <a href="/A216413/b216413.txt">Table of n, a(n) for n = 0..150</a>
%F E.g.f.: Product_{n>=1} (1 + n^(n2)*x^n/n!).
%p a:= n> n!*coeff(series(mul(1+k^(k2)*x^k/k!, k=1..n), x, n+1), x, n):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 07 2012
%t nn=20;p=Product[1+n^(n2)x^n/n!,{n,1,nn}];Range[0,nn]! CoefficientList[Series[p,{x,0,nn}],x]
%Y Cf. A001858.
%K nonn
%O 0,4
%A _Geoffrey Critzer_, Sep 07 2012
