OFFSET
0,2
FORMULA
G.f.: Product_{k>=1} ((1 + 2^(k+1)*(9*x)^k) * (1 + 2^(k-1)*(9*x)^k))^(1/3).
a(n) ~ (-1)^(n+1) * c * 36^n / n^(4/3), where c = 0.244280405759762854740979712556383125782589356973734984...
MATHEMATICA
nmax = 25; CoefficientList[Series[Product[(1+2^(k+1)*x^k)*(1+2^(k-1)*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 25; CoefficientList[Series[Product[(1+2^(k+1)*(9*x)^k)*(1+2^(k-1)*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
nmax = 25; CoefficientList[Series[(2*QPochhammer[-2, 2*x]*QPochhammer[-1/2, 2*x]/9)^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 25; CoefficientList[Series[(2*QPochhammer[-2, x]*QPochhammer[-1/2, x]/9)^(1/3), {x, 0, nmax}], x] * 18^Range[0, nmax]
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Mar 01 2024
STATUS
approved