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A255613
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G.f.: Product_{k>=1} 1/(1-x^k)^(6*k).
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8
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1, 6, 33, 146, 588, 2160, 7459, 24354, 76071, 228420, 663177, 1868220, 5124224, 13718748, 35932278, 92242982, 232473006, 575971494, 1404600837, 3375138816, 7998932769, 18712911214, 43246451181, 98799885342, 223269183076, 499357990254, 1105934610042
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1-x^k)^(6*k).
a(n) ~ 2^(1/6) * Zeta(3)^(1/3) * exp(1/2 + 2^(-1/3) * 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^6 * 3^(1/6) * sqrt(Pi) * n^(5/6)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - Vaclav Kotesovec, Feb 28 2015
G.f.: exp(6*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 29 2018
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, 6*add(
a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
end:
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MATHEMATICA
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nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(6*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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EXTENSIONS
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STATUS
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approved
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