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

0,4

Links

Table of n, a(n) for n=0..94.

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

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.

Prog

(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))

Crossrefs

Cf. A375106, A375107.

Sequence in context: A298141 A160210 A174610 * A373924 A028928 A343723

Adjacent sequences: A375105 A375106 A375107 * A375109 A375110 A375111

Keyword

sign

Author

Seiichi Manyama, Jul 30 2024

Status

approved