A375149 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+4)).

1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 3, 1, -1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 2, 1, -1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 3, 1, -1, 1, 2, 0, 1, 1, 0, 2, 1, 0, 0, 1, -1, 1, 3, 1, 1, 1, 2, 0, 0, 0, 3, 1, -1, 1, 2, -1, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 3, 0, 2, 1, 0, 1, 0, 0, 3, 1, -1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, -1, 0, 5

Offset: 0

Author

Seiichi Manyama, Aug 01 2024

Keywords

• sign

Crossrefs

Cf. A374900, A375106, A375148, A375150.

Programs

PARI

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

PARI

my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-2))*(1-x^(7*k-5)))^2/(1-x^k)))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-2)) * (1-x^(7*k-5)))^2 / (1-x^k).

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