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A027906
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Expansion of Product_{m>=1} (1+q^m)^(4*m).
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9
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1, 4, 14, 48, 141, 396, 1058, 2696, 6646, 15884, 36956, 83976, 186849, 407864, 875030, 1847824, 3845520, 7895872, 16010610, 32088120, 63611656, 124817444, 242560418, 467095640, 891754784, 1688619460
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OFFSET
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0,2
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COMMENTS
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In general, if g.f. = Product_{m>=1} (1+x^m)^(t*m) and t>=1, then a(n) ~ 2^(-2/3 - t/12) * exp((3/2)^(4/3) * t^(1/3) * Zeta(3)^(1/3) * n^(2/3)) * t^(1/6) * Zeta(3)^(1/6) / (3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Aug 17 2015
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LINKS
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FORMULA
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a(n) ~ exp(2^(-2/3) * 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(2/3) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Aug 17 2015
G.f.: exp(4*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[(1+x^k)^(4*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 17 2015 *)
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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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