OFFSET
0,2
COMMENTS
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/3, g(n) = 9.
In general, if h > 1 and g.f. = Product_{k>=1} 1/(1 - h^2*x^k)^(1/h), then a(n) ~ h^(2*n) / (Gamma(1/h) * QPochhammer[1/h^2]^(1/h) * n^(1 - 1/h)). - Vaclav Kotesovec, Apr 22 2018
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * 3^(2*n) / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer[1/9]^(1/3)) = 0.390040743840141117482137514... - Vaclav Kotesovec, Apr 22 2018
MAPLE
seq(coeff(series(mul(1/(1-9*x^k)^(1/3), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 22 2018
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - 9*x^k)^(1/3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 22 2018
STATUS
approved