OFFSET
0,2
FORMULA
G.f.: Product_{k>=1} ((1 + 2*(9*x)^k)/(1 - 2*(9*x)^k))^(1/3).
a(n) ~ QPochhammer(-1, 1/2)^(1/3) * 18^n / (Gamma(1/3) * QPochhammer(1/2)^(1/3) * n^(2/3)).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[(1 + 2*(9*x)^k)/(1 - 2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 29 2024
STATUS
approved