A375158 Expansion of Sum_{k in Z} x^(2*k) / (1 - x^(7*k+2)).

1, 0, 2, -1, 2, 0, 2, 0, 0, 0, 2, 1, 2, -2, 2, 0, 2, 0, 0, 0, 3, 0, 2, -2, 2, 0, 2, 0, 0, 2, 2, 0, 0, -2, 2, 0, 3, 0, 2, 0, 2, 0, 2, -2, 0, 0, 2, 2, 0, 0, 2, -1, 4, -2, 2, 0, 2, 0, 0, 0, 2, 0, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 4, 1, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, -2, 2, 0, 2, -2, 2, 0, 1, 0, 2, 0, 4

Offset: 0

Author

Seiichi Manyama, Aug 01 2024

Keywords

• sign

Crossrefs

Cf. A375107, A375148, A375159.

Cf. A374900, A375108.

Programs

PARI

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

PARI

my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2*(1-x^(7*k-3))*(1-x^(7*k-4))/((1-x^(7*k-2))*(1-x^(7*k-5)))^2))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-3)) * (1-x^(7*k-4)) / ((1-x^(7*k-2)) * (1-x^(7*k-5)))^2.