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A285460
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Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k))^k.
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6
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1, 1, 3, 6, 14, 25, 51, 92, 175, 308, 554, 957, 1670, 2820, 4778, 7940, 13169, 21511, 35032, 56405, 90453, 143716, 227342, 356950, 557977, 866588, 1340109, 2060912, 3156274, 4810016, 7301490, 11034661, 16614681, 24916208, 37234864, 55440054, 82274277
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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 * 2^(-8/3) * (67*Zeta(3))^(1/3) * n^(2/3)) * (67*Zeta(3))^(7/36) / (A * 2^(14/9) * 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^(4*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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