A375106 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+3)).

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

Offset

0,7

Links

Table of n, a(n) for n=0..95.

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))).

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

Prog

(PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=-N, N, x^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)))))

Crossrefs

Cf. A374900, A375148, A375149, A375150.

Cf. A375107, A375108.

Sequence in context: A199322 A351567 A284203 * A341594 A368774 A005087

Adjacent sequences: A375103 A375104 A375105 * A375107 A375108 A375109

Keyword

nonn

Author

Seiichi Manyama, Jul 30 2024

Status

approved