A375107 Expansion of Sum_{k in Z} x^(2*k) / (1 - x^(7*k+3)).

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

Offset

0,13

Links

Table of n, a(n) for n=0..96.

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-3)) * (1-x^(7*k-4))).

G.f.: Sum_{k in Z} x^(3*k) / (1 - x^(7*k+2)).

Prog

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

Crossrefs

Cf. A375106, A375108.

Sequence in context: A336562 A067255 A065716 * A079409 A369461 A114643

Adjacent sequences: A375104 A375105 A375106 * A375108 A375109 A375110

Keyword

sign

Author

Seiichi Manyama, Jul 30 2024

Status

approved