A375150 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+5)).

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

Offset: 0

Author

Seiichi Manyama, Aug 01 2024

Keywords

• sign

Crossrefs

Cf. A374900, A375106, A375148, A375149.

Cf. A375107.

Programs

PARI

my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+5))))

PARI

my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2/((1-x^(7*k-2))*(1-x^(7*k-5)))))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 / ((1-x^(7*k-2)) * (1-x^(7*k-5))).

G.f.: Sum_{k in Z} x^(5*k) / (1 - x^(7*k+1)).