%I A052746
%S A052746 0,1,4,36,512,10000,248832,7529536,268435456,11019960576,
%T A052746 512000000000,26559922791424,1521681143169024,95428956661682176,
%U A052746 6502111422497947648,478296900000000000000,37778931862957161709568
%N A052746 a(0) = 0; a(n) = (2*n)^(n-1), n>0.
%C A052746 Expansion of inverse of x*exp(2x).
%C A052746 Number of well-colored directed trees on n nodes. Well-colored means, 
               each green vertex has at least a red child, each red vertex has no 
               red child.
%H A052746 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=702">
               Encyclopedia of Combinatorial Structures 702</a>
%H A052746 C. Banderier, J.-M. Le Bars and V. Ravelomanana, <a href="http://arxiv.org/
               abs/math.CO/0411138">Generating functions for kernels of digraphs</
               a>
%F A052746 E.g.f.: -1/2*LambertW(-2*x)
%p A052746 spec := [S,{B=Set(S),S=Prod(Z,B,B)},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%o A052746 (Other) SAGE:[lucas_number1(n, 2*n, 0) for n in xrange(0, 17)] [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2009]
%Y A052746 Cf. A038057.
%Y A052746 Cf. A097627.
%Y A052746 Sequence in context: A138435 A008546 A024253 this_sequence A145084 A098629 
               A070780
%Y A052746 Adjacent sequences: A052743 A052744 A052745 this_sequence A052747 A052748 
               A052749
%K A052746 easy,nonn
%O A052746 0,3
%A A052746 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052746 New description from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2003