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A285462
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Expansion of Product_{k>=1} ((1 + x^(2*k)) / (1 - x^k))^k.
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5
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1, 1, 4, 7, 18, 32, 72, 127, 257, 454, 861, 1497, 2719, 4654, 8171, 13781, 23564, 39159, 65559, 107455, 176712, 286000, 463200, 740910, 1184123, 1873656, 2959376, 4636145, 7245680, 11246590, 17409731, 26792371, 41114202, 62769820, 95553779, 144803917
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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) ~ exp(1/12 + 3 * (19*Zeta(3))^(1/3) * n^(2/3) / 4) * (19*Zeta(3))^(7/36) / (A * 2^(7/6) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[((1+x^(2*k))/(1-x^k))^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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