A375159 Expansion of Sum_{k in Z} x^(4*k) / (1 - x^(7*k+2)).

1, -1, 1, 0, 1, 0, 0, -1, 2, 0, 0, -1, 2, 0, 1, 0, -1, 0, 1, -1, 2, -1, 1, 0, 3, -1, -1, 0, 0, 0, 1, -1, 2, 0, 0, 1, 0, -1, 1, 0, 2, -1, 1, -1, 2, -1, -1, 0, 2, 0, 1, -1, 0, 0, 1, -1, 1, 1, 2, 0, 2, -2, 0, 0, -1, 0, -1, 0, 3, 0, 0, -1, 3, -1, 1, 0, 0, 0, 1, -1, 2, 0, 0, -1, 2, 0, -1, 0, 0, 0, 2, -2, 2, 0, 2, 0, -1, -1, 1, 0, 0

Offset: 0

Author

Seiichi Manyama, Aug 01 2024

Keywords

• sign

Crossrefs

Cf. A375107, A375148, A375158.

Cf. A375149.

Programs

PARI

my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^(4*k)/(1-x^(7*k+2))))

PARI

my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-1))*(1-x^(7*k-6)))^2/(1-x^k)))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-1)) * (1-x^(7*k-6)))^2 / (1-x^k).

G.f.: Sum_{k in Z} x^(2*k) / (1 - x^(7*k+4)).