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A301542
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Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_4(k)).
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9
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1, 1, 18, 100, 526, 2546, 12953, 60929, 282194, 1265959, 5580958, 24057117, 101922204, 424244720, 1739362261, 7027590168, 28017627428, 110295521903, 429110693519, 1650961520518, 6285554480496, 23693047787961, 88469251486817, 327380976530282, 1201122749057307
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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(2^(3/2) * 3^(2/3) * Pi * (Zeta(5)/7)^(1/6) * n^(5/6)/5 + Pi * (7/Zeta(5))^(1/6) * n^(1/6) / (240 * sqrt(2) * 3^(2/3)) - 3*Zeta(5) / (8*Pi^4)) * Zeta(5)^(1/12) / (2^(3/4) * 3^(2/3) * 7^(1/12) * n^(7/12)).
G.f.: exp(Sum_{k>=1} sigma_5(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 26 2018
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[4, 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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