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A262811
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Expansion of Product_{k>=1} 1/(1-x^(2*k-1))^(2*k-1).
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18
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1, 1, 1, 4, 4, 9, 15, 22, 37, 56, 92, 133, 210, 310, 466, 696, 1013, 1495, 2160, 3141, 4495, 6462, 9172, 13024, 18387, 25840, 36213, 50500, 70280, 97302, 134522, 185105, 254245, 347938, 475036, 646676, 878145, 1189468, 1607095, 2166672, 2913794, 3910741
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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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a(n) ~ exp(-1/12 + 3*Zeta(3)^(1/3)*n^(2/3)/2) * A * Zeta(3)^(5/36) / (2^(2/3) * sqrt(3*Pi) * n^(23/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
`if`(d::even, 0, d), d=divisors(j))*a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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nmax = 60; CoefficientList[Series[Product[1/(1-x^(2*k-1))^(2*k-1), {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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