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Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+5)).
5

%I #11 Aug 01 2024 14:13:16

%S 1,0,1,0,1,1,1,-1,1,0,2,0,1,0,1,1,0,0,1,-1,2,1,1,0,1,0,1,0,1,0,2,-1,1,

%T 0,0,1,1,1,1,0,3,0,0,-2,1,1,1,0,1,0,2,0,0,1,1,0,1,0,1,1,2,-1,1,0,1,0,

%U 1,-1,0,1,2,0,1,0,1,1,1,0,2,-2,2,0,1,0,1,2,1,0,-1,0,2,-1,1,0,0,1,1,0,1,0,3

%N Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+5)).

%F G.f.: Product_{k>0} (1-x^(7*k))^2 / ((1-x^(7*k-2)) * (1-x^(7*k-5))).

%F G.f.: Sum_{k in Z} x^(5*k) / (1 - x^(7*k+1)).

%o (PARI) my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+5))))

%o (PARI) my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2/((1-x^(7*k-2))*(1-x^(7*k-5)))))

%Y Cf. A374900, A375106, A375148, A375149.

%Y Cf. A375107.

%K sign

%O 0,11

%A _Seiichi Manyama_, Aug 01 2024