OFFSET
0,2
FORMULA
G.f.: Product_{k>=1} (1 + 3*(3*x)^k)^(1/3).
a(n) ~ (-1)^(n+1) * c * 9^n / n^(4/3), where c = QPochhammer(-1/3)^(1/3) / (3*Gamma(2/3)) = 0.26286302373105271371291957730496322329245126572...
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 + 3*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 3^Range[0, nmax]
nmax = 30; CoefficientList[Series[Product[(1 + 3*(3*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
nmax = 30; CoefficientList[Series[(QPochhammer[-3, x]/4)^(1/3), {x, 0, nmax}], x] * 3^Range[0, nmax]
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Feb 27 2024
STATUS
approved