A279932 revision #18
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A279932
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Expansion of Product_{k>0} 1/(1 + x^k)^(k*5).
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4
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1, -5, 5, 0, 30, -51, 5, -130, 220, -125, 649, -605, 870, -2695, 1565, -4852, 7915, -6360, 20625, -17880, 33551, -61015, 50865, -138510, 135485, -224725, 389025, -359610, 849525, -838970, 1417404, -2195205, 2275690, -4756040, 4657940, -8315123, 11174840, -13352315
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OFFSET
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0,2
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COMMENTS
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In general, if m >= 1 and g.f. = Product_{k>=1} 1/(1 + x^k)^(m*k), then a(n, m) ~ (-1)^n * exp(-m/12 + 3 * 2^(-5/3) * m^(1/3) * Zeta(3)^(1/3) * n^(2/3)) * 2^(m/18 - 5/6) * A^m * m^(1/6 - m/36) * Zeta(3)^(1/6 - m/36) * n^(m/36 - 2/3) / sqrt(3*Pi), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 13 2017
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LINKS
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FORMULA
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a(n) ~ (-1)^n * exp(-5/12 + 3 * 2^(-5/3) * (5*Zeta(3))^(1/3) * n^(2/3)) * A^5 * (5*Zeta(3))^(1/36) / (2^(5/9) * sqrt(3*Pi) * n^(19/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 13 2017
G.f.: exp(5*Sum_{k>=1} (-1)^k*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, Mar 27 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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reviewed
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