OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} 1/(1 + (-1)^(k*(k+1)/2) * x^k).
G.f.: Product_{k>=1} (1 + x^(4*k-2)) / ((1 + x^(4*k-1)) * (1 - x^(4*k-3))).
a(n) ~ Gamma(1/4) * exp(Pi*sqrt(n/6)) / (4 * 6^(1/8) * Pi^(3/4) * n^(5/8)). - Vaclav Kotesovec, Jul 17 2019
MATHEMATICA
nmax = 70; CoefficientList[Series[Product[1/(1 + (-1)^(k (k + 1)/2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k - 2))/((1 + x^(4 k - 1)) (1 - x^(4 k - 3))), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[2/(QPochhammer[-1, -x^2] QPochhammer[x, -x^2]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 17 2019
STATUS
approved