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A285291
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Expansion of Product_{k>=1} ((1 + x^k) / (1 + x^(5*k)))^k.
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5
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1, 1, 2, 5, 8, 15, 27, 47, 78, 134, 218, 356, 576, 916, 1449, 2268, 3525, 5431, 8324, 12652, 19129, 28754, 42974, 63898, 94553, 139241, 204144, 298045, 433328, 627592, 905560, 1301934, 1865362, 2663816, 3791813, 5380911, 7613286, 10740839, 15111141, 21202615
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OFFSET
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0,3
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COMMENTS
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In general, if m > 1 and g.f. = Product_{k>=1} ((1 + x^k) / (1 + x^(m*k)))^k, then a(n, m) ~ exp(2^(-4/3) * 3^(4/3) * (1-1/m^2)^(1/3) * Zeta(3)^(1/3) * n^(2/3)) * ((1-1/m^2)*Zeta(3))^(1/6) / (2^(2/3) * 3^(1/3) * sqrt(Pi) * n^(2/3)).
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LINKS
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FORMULA
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a(n) ~ exp(2^(-1/3) * 3^(5/3) * 5^(-2/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (5^(1/3) * 6^(1/6) * sqrt(Pi) * n^(2/3)).
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1+x^(5*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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