A375108 - OEIS

%I #13 Jul 30 2024 14:41:18

%S 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,

%T 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,

%U 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

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

%H R. P. Agarwal, <a href="https://www.ias.ac.in/describe/article/pmsc/103/03/0269-0293">Lambert series and Ramanujan</a>, Prod. Indian Acad. Sci. (Math. Sci.), v. 103, n. 3, 1993, pp. 269-293. see p. 286.

%F 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.

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

%o (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))

%Y Cf. A375106, A375107.

%K sign

%O 0,4

%A _Seiichi Manyama_, Jul 30 2024