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A097631
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Number of unrooted directed trees on n nodes with a green root.
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1
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0, 1, 5, 58, 907, 19046, 496869, 15578130, 570573623, 23929861102, 1131235173433, 59529368839898, 3451899685313523, 218712237867226182, 15034642075916533997, 1114519318895861250082, 88631119148029975177327, 7526795487859400166772958, 679859967684397018073935617
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) ~ 2^(n-1) * n^(n-2) * (1 - LambertW(1/2)) / (1 + LambertW(1/2)). - Vaclav Kotesovec, Feb 24 2019
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MATHEMATICA
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(* Note: Mathematica's ProductLog is the Lambert W function. *)
a[n_] := SeriesCoefficient[-ProductLog[-ProductLog[-2x]/2]/n - ProductLog[-2x] (ProductLog[-2x] + 2)/4, {x, 0, n}] n!;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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