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A097630 Number of unrooted directed trees on n nodes with a red root. 3
1, 1, 7, 70, 1093, 22426, 578779, 17976302, 653866441, 27270138898, 1283303262151, 67277393090854, 3888789288662029, 245724292311198650, 16851817924083466003, 1246663922538961356766, 98960637955717312632721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

C. Banderier, J.-M. Le Bars and V. Ravelomanana, Generating functions for kernels of digraphs

FORMULA

E.g.f.: A(x) = 2B - 2BC + C - 2B/C + C^2/2, with B = egf of A052746 and C = egf of A097627.

a(n) = (n-1)!*[x^n](LambertW(-LambertW(-2x)/2)). - Jean-François Alcover, Dec 13 2018

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

MATHEMATICA

terms = 17;

Rest[CoefficientList[LambertW[-LambertW[-2x]/2] + O[x]^(terms+1), x]]* Range[0, terms-1]! (* Jean-François Alcover, Dec 13 2018 *)

PROG

(PARI) seq(n)={Vec(serlaplace(lambertw(-lambertw(-2*x + O(x*x^n))/2)/x))} \\ Andrew Howroyd, Dec 13 2018

CROSSREFS

Cf. A097629.

Sequence in context: A141151 A001669 A051604 * A090647 A200929 A111462

Adjacent sequences:  A097627 A097628 A097629 * A097631 A097632 A097633

KEYWORD

nonn

AUTHOR

Ralf Stephan, Aug 17 2004

STATUS

approved

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Last modified July 25 22:19 EDT 2021. Contains 346294 sequences. (Running on oeis4.)