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%I #7 Feb 06 2014 03:25:19
%S 3,24,450,13464,555210,29218212,1871592534,141327100080,
%T 12293325631602,1210526420471100,133114686648358734,
%U 16168770752009690376,2149972767937717220394,310628961824895629954388,48456042707642573220000390,8116814004435897170203179360
%N E.g.f. A(x) satisfies A(x) = x*(2*exp(A(x)) + exp(2*A(x))).
%F a(n) ~ sqrt(s/(3-2*s)) * n^(n-1) / (exp(n) * r^n), where s = 0.6693241011832267063... is the root of the equation (2-1/s)*(2+exp(s)) = 2, and r = s*exp(-s)/(2+exp(s)) = 0.08670317777647875508... - _Vaclav Kotesovec_, Jan 26 2014
%t Rest[CoefficientList[InverseSeries[Series[(x/(E^x*(2+E^x))),{x,0,20}],x],x]*Range[0,20]!]
%t Table[Sum[2^j*(2*n-j)^(n-1)*Binomial[n,j],{j,0,n}],{n,1,20}]
%Y Cf. A200904.
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Jan 26 2014
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