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A285293
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Expansion of Product_{k>=1} (1 + x^k)^k / (1 + x^(5*k))^(5*k).
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4
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1, 1, 2, 5, 8, 11, 23, 39, 58, 102, 160, 250, 392, 614, 929, 1426, 2155, 3221, 4816, 7124, 10516, 15389, 22448, 32549, 47027, 67586, 96779, 138052, 196078, 277606, 391570, 550516, 771442, 1077818, 1501214, 2084899, 2887759, 3988792, 5495381, 7552127, 10353345
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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)^k / (1 + x^(m*k))^(m*k), then a(n, m) ~ exp(2^(-4/3) * 3^(4/3) * (1-1/m)^(1/3) * Zeta(3)^(1/3) * n^(2/3)) * 2^(m/12 - 3/4) * (1-1/m)^(1/6) * Zeta(3)^(1/6) / (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^(-2/3) * 3^(4/3) * 5^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (3^(1/3) * 5^(1/6) * sqrt(Pi) * n^(2/3)).
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1+x^k)^k/(1+x^(5*k))^(5*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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