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URL: https://oeis.org/A258346

⇱ A258346 - OEIS

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A258346
Expansion of Product_{k>=1} (1+x^k)^(k*(k-1)*(k-2)/6).
8
1, 0, 0, 1, 4, 10, 20, 39, 72, 144, 280, 567, 1112, 2187, 4204, 8073, 15309, 28986, 54548, 102286, 190881, 354717, 656194, 1208712, 2217624, 4052633, 7379630, 13390098, 24215587, 43649482, 78435884, 140513905, 250988186, 447037367, 794031641, 1406585604
OFFSET
0,5
LINKS
FORMULA
a(n) ~ (3*Zeta(5))^(1/10) / (2^(523/720) * 5^(2/5) * sqrt(Pi) * n^(3/5)) * exp(-2401 * Pi^16 / (10497600000000 * Zeta(5)^3) + 49*Pi^8 * Zeta(3) / (16200000 * Zeta(5)^2) - Zeta(3)^2 / (150*Zeta(5)) + (-343*Pi^12 / (2430000000 * 2^(3/5) * 15^(1/5) * Zeta(5)^(11/5)) + 7*Pi^4 * Zeta(3) / (4500 * 2^(3/5) * 15^(1/5) * Zeta(5)^(6/5))) * n^(1/5) + (-49*Pi^8 / (1080000 * 2^(1/5) * 15^(2/5) * Zeta(5)^(7/5)) + Zeta(3) / (2^(6/5) * (15*Zeta(5))^(2/5))) * n^(2/5) - 7*Pi^4 / (180 * 2^(4/5) * (15*Zeta(5))^(3/5)) * n^(3/5) + 5*(15*Zeta(5))^(1/5) / 2^(12/5) * n^(4/5)), where Zeta(3) = A002117, Zeta(5) = A013663.
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+x^k)^(k*(k-1)*(k-2)/6), {k, 1, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 27 2015
STATUS
approved