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A277470
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E.g.f.: arcsinh(x)/(1+LambertW(-x)).
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3
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0, 1, 2, 11, 104, 1249, 18264, 318163, 6425152, 147344769, 3781848480, 107408279483, 3343875651456, 113227469886881, 4142804357946240, 162871544915116035, 6847004160475236352, 306495323034774157569, 14554502490109085839872, 730777840212988501198059
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ arcsinh(exp(-1)) * n^n.
a(n) ~ (-1 + log(1 + sqrt(1+exp(2)))) * n^n.
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MATHEMATICA
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CoefficientList[Series[ArcSinh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[Sin[Pi*n/2] * (n-2)!!^2 + Sum[Sin[Pi*k/2] * Binomial[n, k] * (k-2)!!^2 * (n-k)^(n-k), {k, 1, n-1}], {n, 1, 25}]}] (* Vaclav Kotesovec, Oct 28 2016 *)
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PROG
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(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(asinh(x)/(1 + lambertw(-x)) ))) \\ G. C. Greubel, Nov 07 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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