A216413 - OEIS

%I #24 Mar 18 2018 15:13:02

%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^(n-2)*x^n/n!).

%p a:= n-> n!*coeff(series(mul(1+k^(k-2)*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^(n-2)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