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A261386
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Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(2*k).
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13
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1, 4, 16, 56, 176, 520, 1456, 3896, 10048, 25100, 60960, 144440, 334752, 760456, 1696464, 3722224, 8043040, 17135624, 36031104, 74840568, 153680928, 312198160, 627828272, 1250540024, 2468443296, 4830809868, 9377190336, 18061370288, 34531009760, 65552873736
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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) ~ exp(1/6 + 3/2*(7*Zeta(3))^(1/3) * n^(2/3)) * (7*Zeta(3))^(2/9) / (A^2 * 2^(2/3) * n^(13/18) * sqrt(3*Pi)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
G.f.: exp(Sum_{k>=1} (sigma_2(2*k) - sigma_2(k))*x^k/k). - Ilya Gutkovskiy, Apr 14 2019
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[(1+x^k)^(2*k) / (1-x^k)^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]
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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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