OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=0} 1 / ((1-x^(4*k+1))^(4*k+1) * (1-x^(4*k+2))^(4*k+2) * (1-x^(4*k+3))^(4*k+3)).
a(n) ~ exp(-1/4 + 2^(-4/3) * 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)) * A^3 * Zeta(3)^(1/12) / (2^(5/4) * 3^(5/12) * sqrt(Pi) * n^(7/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 16 2017
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[1 / ((1-x^(4*k+1))^(4*k+1) * (1-x^(4*k+2))^(4*k+2) * (1-x^(4*k+3))^(4*k+3)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
nmax = 50; CoefficientList[Series[Product[(1 - x^(4*k))^(4*k)/((1 - x^k)^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
PROG
(PARI) x='x+O('x^100); Vec(prod(k=0, 100, 1 / ((1 - x^(4*k + 1))^(4*k + 1)*(1 - x^(4*k + 2))^(4*k + 2)*(1 - x^(4*k + 3))^(4*k + 3)))) \\ Indranil Ghosh, Apr 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2017
STATUS
approved