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
Keywords
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.
Programs
-
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)))))
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)).