OFFSET
0,2
FORMULA
G.f.: Product_{k>=1} (1 + 2*(9*x)^k)^(1/3).
a(n) ~ (-1)^(n+1) * c * 18^n / n^(4/3), where c = QPochhammer(-1/2)^(1/3) / (3*Gamma(2/3)) = 0.2623638446186535909018671540030519...
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 3^(2*Range[0, nmax])
nmax = 20; CoefficientList[Series[Product[(1 + 2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
nmax = 20; CoefficientList[Series[(QPochhammer[-2, x]/3)^(1/3), {x, 0, nmax}], x] * 3^(2*Range[0, nmax])
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Feb 27 2024
STATUS
approved