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A263140
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Expansion of Product_{k>=1} (1 + x^(2*k-1))^k.
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11
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1, 1, 0, 2, 2, 3, 4, 5, 10, 11, 16, 20, 31, 39, 50, 71, 93, 124, 154, 211, 271, 357, 449, 587, 762, 968, 1233, 1571, 2021, 2535, 3220, 4049, 5145, 6431, 8070, 10105, 12670, 15784, 19619, 24447, 30348, 37635, 46464, 57532, 70945, 87477, 107456, 132192, 162220
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: exp(Sum_{j>=1} (-1)^(j+1)/j*x^j/(1 - x^(2*j))^2).
a(n) ~ exp(-Pi^4 / (5184*Zeta(3)) + Pi^2 * n^(1/3) / (8 * 3^(4/3) * Zeta(3)^(1/3)) + 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)/4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3)* sqrt(Pi) * n^(2/3)).
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[(1 + x^(2*k-1))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; CoefficientList[Series[E^Sum[(-1)^(j+1)/j*x^j/(1 - x^(2*j))^2, {j, 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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