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A306081
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Expansion of e.g.f. Product_{k>=1} ((1 + (exp(x) - 1)^k) / (1 - (exp(x) - 1)^k))^k.
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4
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1, 2, 14, 134, 1574, 22262, 367814, 6907574, 144942854, 3357588662, 85000841414, 2331998188214, 68862337593734, 2176283210561462, 73250933670041414, 2614843434740912054, 98632371931151518214, 3918608865052986708662, 163507638190268814991814
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling2(n,k) * A156616(k) * k!.
a(n) ~ n! * exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / (4 * log(2)^(2/3)) + (1 - log(2)) * (7*Zeta(3))^(2/3) * n^(1/3) / (8 * log(2)^(4/3)) - 7*(log(2)^2 + log(2) - 1) * Zeta(3) / (48 * log(2)^2) + 1/12) * (7*Zeta(3))^(7/36) / (A * 2^(13/12) * sqrt(3*Pi) * n^(25/36) * (log(2))^(n + 11/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jun 22 2018
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Product[((1 + (Exp[x] - 1)^k)/(1 - (Exp[x] - 1)^k))^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
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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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