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%I #16 Aug 01 2024 14:13:07
%S 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,
%T 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,
%U 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
%N Expansion of Sum_{k in Z} x^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))).
%F G.f.: Sum_{k in Z} x^(3*k) / (1 - x^(7*k+1)).
%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=-N, N, x^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)))))
%Y Cf. A374900, A375148, A375149, A375150.
%Y Cf. A375107, A375108.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Jul 30 2024
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