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A255612
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G.f.: Product_{k>=1} 1/(1-x^k)^(5*k).
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9
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1, 5, 25, 100, 370, 1251, 4005, 12150, 35400, 99365, 270353, 715025, 1844650, 4652075, 11494605, 27872056, 66428295, 155809600, 360079225, 820715820, 1846583863, 4104572975, 9019869125, 19608423750, 42193733645, 89917531549, 189863358445, 397401303850
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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)^(5*k).
a(n) ~ 5^(11/36) * Zeta(3)^(11/36) * exp(5/12 + 3 * 2^(-2/3) * 5^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (A^5 * 2^(7/36) * sqrt(3*Pi) * n^(29/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... . - Vaclav Kotesovec, Feb 28 2015
G.f.: exp(5*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, 5*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)^(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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EXTENSIONS
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STATUS
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approved
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