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A374900 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+1)).

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%I A374900 #17 Jul 31 2024 14:41:17
%S A374900 1,2,2,2,2,1,2,2,2,3,2,0,2,2,2,2,2,2,2,2,2,2,2,0,1,4,2,2,2,0,2,2,3,4,
%T A374900 2,0,2,0,2,2,2,2,2,2,2,2,2,2,2,4,0,2,2,0,2,2,2,3,2,0,2,2,4,0,2,2,2,2,
%U A374900 2,3,2,0,2,4,2,2,0,0,2,2,2,4,2,0,2,2,2,2,2,0,2,4,4,2,2,0,2,2,2,2,2
%N A374900 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+1)).
%F A374900 G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-2)) * (1-x^(7*k-5)) / ((1-x^(7*k-1)) * (1-x^(7*k-6)))^2.
%o A374900 (PARI) my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+1))))
%o A374900 (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))/((1-x^(7*k-1))*(1-x^(7*k-6)))^2))
%Y A374900 Cf. A008441, A033687, A097195, A340456.
%K A374900 nonn
%O A374900 0,2
%A A374900 _Seiichi Manyama_, Jul 31 2024