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A262947
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Expansion of Product_{k>=1} 1/(1-x^(3*k-2))^(3*k-2).
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10
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1, 1, 1, 1, 5, 5, 5, 12, 22, 22, 32, 60, 80, 93, 161, 231, 282, 404, 616, 775, 1041, 1535, 2037, 2600, 3708, 5029, 6411, 8710, 11968, 15315, 20189, 27444, 35619, 45939, 61605, 80422, 102932, 135481, 177391, 226263, 293561, 382984, 488826, 626558, 812750
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ 2^(23/36) * sqrt(Pi) * Zeta(3)^(5/36) * exp(3*d2 + (3/2)^(2/3) * Zeta(3)^(1/3) * n^(2/3)) / (3^(11/36) * Gamma(1/3)^2 * n^(23/36)), where d2 = A263031 = Integral_{x=0..infinity} 1/x*(exp(-x)/(1 - exp(-3*x))^2 - 1/(9*x^2) - 2/(9*x) - 5*exp(-x)/36) = -0.01453742918328403360502029450226209036054149... . - Vaclav Kotesovec, Oct 08 2015
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
`if`(irem(d+3, 3, 'r')=1, 3*r-2, 0),
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^(3k-2))^(3k-2)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax=60; CoefficientList[Series[E^Sum[1/j*x^j*(1+2*x^(3*j))/(1-x^(3*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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