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A097174
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Total number of red nodes among tricolored labeled trees on n nodes.
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9
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1, 0, 6, 12, 320, 2190, 51492, 685496, 17286768, 348213690, 9956411300, 266065478052, 8737396913544, 287741445880070, 10816320294520860, 420123621828718320, 17913098835916877792, 798053882730994171890, 38192029991097097185108, 1914946396460982552420380
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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) = -T(-T(x)), with T(x) = Sum_{k>=1} A000169(k)/k!*x^k.
a(n) = -n^(n-1) * Sum_{j=1..n} (-j/n)^j*C(n, j).
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MATHEMATICA
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Rest[CoefficientList[Series[LambertW[-LambertW[-x]], {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, Aug 26 2016 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(lambertw(-lambertw(-x)))) \\ 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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