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%I #17 Feb 24 2019 17:16:26
%S 0,1,5,58,907,19046,496869,15578130,570573623,23929861102,
%T 1131235173433,59529368839898,3451899685313523,218712237867226182,
%U 15034642075916533997,1114519318895861250082,88631119148029975177327,7526795487859400166772958,679859967684397018073935617
%N Number of unrooted directed trees on n nodes with a green root.
%H C. Banderier, J.-M. Le Bars and V. Ravelomanana, <a href="https://arxiv.org/abs/math/0411138">Generating functions for kernels of digraphs</a>, arXiv:math/0411138 [math.CO], 2004.
%F a(n) ~ 2^(n-1) * n^(n-2) * (1 - LambertW(1/2)) / (1 + LambertW(1/2)). - _Vaclav Kotesovec_, Feb 24 2019
%t (* Note: Mathematica's ProductLog is the Lambert W function. *)
%t a[n_] := SeriesCoefficient[-ProductLog[-ProductLog[-2x]/2]/n - ProductLog[-2x] (ProductLog[-2x] + 2)/4, {x, 0, n}] n!;
%t Array[a, 17] (* _Jean-François Alcover_, Feb 24 2019 *)
%Y Equals A097629(n) - A097630(n).
%K nonn
%O 1,3
%A _Ralf Stephan_, Aug 17 2004
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