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A097630
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Number of unrooted directed trees on n nodes with a red root.
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3
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1, 1, 7, 70, 1093, 22426, 578779, 17976302, 653866441, 27270138898, 1283303262151, 67277393090854, 3888789288662029, 245724292311198650, 16851817924083466003, 1246663922538961356766, 98960637955717312632721
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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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E.g.f.: A(x) = 2B - 2BC + C - 2B/C + C^2/2, with B = egf of A052746 and C = egf of A097627.
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MATHEMATICA
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terms = 17;
Rest[CoefficientList[LambertW[-LambertW[-2x]/2] + O[x]^(terms+1), x]]* Range[0, terms-1]! (* Jean-François Alcover, Dec 13 2018 *)
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PROG
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(PARI) seq(n)={Vec(serlaplace(lambertw(-lambertw(-2*x + O(x*x^n))/2)/x))} \\ Andrew Howroyd, Dec 13 2018
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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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