A375108 Expansion of Sum_{k in Z} x^(3*k) / (1 - x^(7*k+3)).

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

Offset: 0

Author

Seiichi Manyama, Jul 30 2024

Keywords

• sign

Links

• R. P. Agarwal, Lambert series and Ramanujan, Prod. Indian Acad. Sci. (Math. Sci.), v. 103, n. 3, 1993, pp. 269-293. see p. 286.

Crossrefs

Cf. A375106, A375107.

Programs

PARI

my(N=100, x='x+O('x^N)); Vec(sum(k=-N, N, x^(3*k)/(1-x^(7*k+3))))

PARI

my(N=100, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2*(1-x^(7*k-1))*(1-x^(7*k-6))/((1-x^(7*k-3))*(1-x^(7*k-4)))^2))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-1)) * (1-x^(7*k-6)) / ((1-x^(7*k-3)) * (1-x^(7*k-4)))^2.