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%I #7 Aug 26 2016 02:35:40
%S 0,2,0,48,120,4560,35700,1048992,15514128,456726240,10073339100,
%T 323266492560,9361060088952,336767513038320,11913610172869860,
%U 482920107426039360,19998225191360977440,909512248720724321472
%N Total number of green nodes among tricolored labeled trees on n nodes.
%H S. Coulomb and M. Bauer, <a href="http://arXiv.org/abs/math.CO/0407456">On vertex covers, matchings and random trees</a>
%F E.g.f.: A(x) = T(-T(x))^2, with T(x)=Sum[k=1..inf, A000169(k)/k!*x^k].
%F a(n) = -2 * n^(n-1) * Sum[l=1..n, (-l/n)^l*(1/l-1)*C(n, l)].
%F a(n) ~ 2*LambertW(1)^2*n^(n-1)/(1+LambertW(1)). - _Vaclav Kotesovec_, Aug 26 2016
%t Rest[CoefficientList[Series[LambertW[-LambertW[-x]]^2, {x, 0, 20}], x] * Range[0, 20]!] (* _Vaclav Kotesovec_, Aug 26 2016 *)
%Y Cf. A097170, A097171, A097172, A097174, A000272.
%K nonn
%O 1,2
%A _Ralf Stephan_, Jul 30 2004
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