OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ 3^(1/5) * Zeta(5)^(1/10) / (2^(91/120) * 5^(2/5) * sqrt(Pi) * n^(3/5)) * exp(-2401 * Pi^16 / (1749600000000*Zeta(5)^3) + 49 * Pi^8 * Zeta(3) / (2700000 * Zeta(5)^2) - Zeta(3)^2 / (25*Zeta(5)) + (-343 * Pi^12 / (405000000 * 2^(4/5) * 3^(2/5) * 5^(1/5) * Zeta(5)^(11/5)) + 7*Pi^4 * Zeta(3) / (750 * 2^(4/5) * 3^(2/5) * 5^(1/5) * Zeta(5)^(6/5))) * n^(1/5) + (-49*Pi^8 / (180000 * 2^(3/5) * 3^(4/5) * 5^(2/5) * Zeta(5)^(7/5)) + 3^(1/5) * Zeta(3) / (2^(3/5) * (5*Zeta(5))^(2/5))) * n^(2/5) - 7*Pi^4 / (180 * 2^(2/5) * 3^(1/5) * (5*Zeta(5))^(3/5)) * n^(3/5) + 5*3^(2/5) * ((5*Zeta(5))/2)^(1/5)/4 * n^(4/5)), where Zeta(3) = A002117, Zeta(5) = A013663.
MATHEMATICA
nmax=40; CoefficientList[Series[Product[(1+x^k)^(k*(k-1)*(k-2)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 27 2015
STATUS
approved