A303348 Expansion of Product_{n>=1} (1 - 9*x^n)^(1/3).

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

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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).

Cf. A303349, A303351.

Sequence in context: A122994 A271218 A062311 * A237036 A034956 A032093

Adjacent sequences: A303345 A303346 A303347 * A303349 A303350 A303351

Keyword

sign

Author

Seiichi Manyama, Apr 22 2018

Status

approved