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A097631 Number of unrooted directed trees on n nodes with a green root. 1
0, 1, 5, 58, 907, 19046, 496869, 15578130, 570573623, 23929861102, 1131235173433, 59529368839898, 3451899685313523, 218712237867226182, 15034642075916533997, 1114519318895861250082, 88631119148029975177327, 7526795487859400166772958, 679859967684397018073935617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..19.

C. Banderier, J.-M. Le Bars and V. Ravelomanana, Generating functions for kernels of digraphs, arXiv:math/0411138 [math.CO], 2004.

FORMULA

a(n) ~ 2^(n-1) * n^(n-2) * (1 - LambertW(1/2)) / (1 + LambertW(1/2)). - Vaclav Kotesovec, Feb 24 2019

MATHEMATICA

(* 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!;

Array[a, 17] (* Jean-Fran├žois Alcover, Feb 24 2019 *)

CROSSREFS

Equals A097629(n) - A097630(n).

Sequence in context: A129897 A256218 A151424 * A130768 A195947 A156326

Adjacent sequences:  A097628 A097629 A097630 * A097632 A097633 A097634

KEYWORD

nonn

AUTHOR

Ralf Stephan, Aug 17 2004

STATUS

approved

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Last modified August 1 10:37 EDT 2021. Contains 346385 sequences. (Running on oeis4.)