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A097627
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Number of rooted directed trees on n nodes with a red root.
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5
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1, 2, 21, 280, 5465, 134556, 4051453, 143810416, 5884797969, 272701388980, 14116335883661, 807328717090248, 50554260752606377, 3440140092356781100, 252777268861251990045, 19946622760623381708256
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OFFSET
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1,2
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COMMENTS
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Ditrees are well-colored directed trees. Well-colored means, each green vertex has at least a red child, each red vertex has no red child.
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LINKS
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FORMULA
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E.g.f.: -C(-C(2*x)/2), where C(x) is the e.g.f. of A000169.
a(n) ~ LambertW(1/2) * n^(n-1) * 2^n / (1+LambertW(1/2)). - Vaclav Kotesovec, Oct 08 2013
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MATHEMATICA
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Rest[CoefficientList[Series[LambertW[-LambertW[-2*x]/2], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 08 2013 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(lambertw(-lambertw(-2*x)/2))) \\ G. C. Greubel, Nov 15 2017
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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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