login
A303348
Expansion of Product_{n>=1} (1 - 9*x^n)^(1/3).
3
1, -3, -12, -39, -246, -1578, -11487, -84054, -635781, -4893357, -38292969, -303553209, -2432865630, -19678331838, -160427322399, -1316796234933, -10872602692581, -90242886252945, -752488383572787, -6300541703215803, -52949782408528290
OFFSET
0,2
COMMENTS
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/3, g(n) = 9.
LINKS
FORMULA
a(n) ~ -c * 3^(2*n-1) / (Gamma(2/3) * n^(4/3)), where c = QPochhammer[1/9]^(1/3) = 0.95703379660353017269195329... - Vaclav Kotesovec, Apr 25 2018
MAPLE
seq(coeff(series(mul((1-9*x^k)^(1/3), k=1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 22 2018
PROG
(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-9*x^k)^(1/3)))
CROSSREFS
Expansion of Product_{n>=1} (1 - b^2*x^n)^(1/b): A010815 (b=1), A303347 (b=2), this sequence (b=3).
Sequence in context: A122994 A271218 A062311 * A237036 A034956 A373301
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 22 2018
STATUS
approved