cp's OEIS Frontend

A218691 Number of ways to paint some (possibly none or all) of the trees over all forests on n labeled nodes.

%I A218691 #16 Dec 29 2014 19:40:16
%S A218691 1,2,6,26,156,1242,12616,158034,2372880,41725106,843126624,
%T A218691 19277549898,492447987136,13907344659210,430397513894016,
%U A218691 14487404695687298,527023721684738304,20605894357093102434,861761850029367846400,38387125875316048363386,1814541564588778500135936
%N A218691 Number of ways to paint some (possibly none or all) of the trees over all forests on n labeled nodes.
%H A218691 Alois P. Heinz, <a href="/A218691/b218691.txt">Table of n, a(n) for n = 0..150</a>
%F A218691 E.g.f.: exp(T(x) - T(x)^2/2)^2 where T(x) is e.g.f. for A000169.
%F A218691 a(n) = Sum_{m=1..n} A105599(n,m)*2^m.
%F A218691 a(n) ~ 2*n^(n-2)*exp(1). - _Vaclav Kotesovec_, Aug 16 2013
%p A218691 T:= -LambertW(-x):
%p A218691 egf:= exp(T-T^2/2)^2:
%p A218691 a:= n-> n! * coeff(series(egf, x, n+1), x, n):
%p A218691 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 04 2012
%t A218691 nn=20;t=Sum[n^(n-1)x^n/n!,{n,1,nn}];Range[0,nn]!CoefficientList[ Series[Exp[(t-t^2/2)]^2,{x,0,nn}],x]
%Y A218691 Cf. A101313.
%K A218691 nonn
%O A218691 0,2
%A A218691 _Geoffrey Critzer_, Nov 04 2012