A375158 - OEIS

%I #6 Aug 01 2024 23:16:42

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

%T -2,2,0,3,0,2,0,2,0,2,-2,0,0,2,2,0,0,2,-1,4,-2,2,0,2,0,0,0,2,0,2,-2,2,

%U 2,2,0,0,0,0,0,2,-2,4,1,2,0,0,0,0,0,2,0,4,0,2,0,0,-2,2,0,2,-2,2,0,1,0,2,0,4

%N Expansion of Sum_{k in Z} x^(2*k) / (1 - x^(7*k+2)).

%F G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-3)) * (1-x^(7*k-4)) / ((1-x^(7*k-2)) * (1-x^(7*k-5)))^2.

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

%o (PARI) my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2*(1-x^(7*k-3))*(1-x^(7*k-4))/((1-x^(7*k-2))*(1-x^(7*k-5)))^2))

%Y Cf. A375107, A375148, A375159.

%Y Cf. A374900, A375108.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 01 2024