A303398 Expansion of Product_{k>=1} (1 - 3*x^k)/(1 + 3*x^k).

1, -6, 12, -24, 102, -312, 840, -2544, 7788, -23406, 69816, -208968, 628536, -1886712, 5654784, -16961856, 50900934, -152709936, 458084244, -1374231912, 4122828408, -12368549040, 37105252680, -111315549552, 333947845416, -1001844169854, 3005528872008

Offset: 0

Author

Seiichi Manyama, Apr 23 2018

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..2094

Crossrefs

Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), A303397 (b=2), this sequence (b=3), A303402 (b=4).

Cf. A303390.

Programs

Maple

N:= 100: # for a(0)..a(N)
G:= mul((1-3*x^k)/(1+3*x^k),k=1..N):
S:= series(G,x,N+1):
seq(coeff(S,x,n),n=0..N); # Robert Israel, Jul 31 2020

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - 3*x^k)/(1 + 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-3*x^k)/(1+3*x^k)))

Formula

a(n) ~ c * (-3)^n, where c = QPochhammer[-1, -1/3]/QPochhammer[-1/3] = 1.1824106844873309732830080836112464096086... - Vaclav Kotesovec, Apr 25 2018