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Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+4)).
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%I #11 Aug 01 2024 14:13:12

%S 1,1,0,1,2,0,1,1,0,1,1,0,3,1,-1,1,2,0,0,1,1,1,1,1,2,1,-1,1,2,0,1,0,0,

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

%U -1,1,2,0,1,0,0,2,1,0,1,3,0,2,1,0,1,0,0,3,1,-1,1,0,1,1,1,1,1,1,0,1,1,-1,0,5

%N Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+4)).

%F G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-2)) * (1-x^(7*k-5)))^2 / (1-x^k).

%F G.f.: Sum_{k in Z} x^(4*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+4))))

%o (PARI) my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-2))*(1-x^(7*k-5)))^2/(1-x^k)))

%Y Cf. A374900, A375106, A375148, A375150.

%K sign

%O 0,5

%A _Seiichi Manyama_, Aug 01 2024