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Expansion of 1 / Sum_{k in Z} x^k / (1 - x^(5*k+2)).
3

%I #11 Jul 29 2024 09:59:13

%S 1,-1,0,0,-1,3,-3,1,0,-3,9,-9,3,1,-9,22,-22,9,2,-22,51,-51,22,6,-51,

%T 108,-108,50,13,-108,221,-221,105,29,-220,429,-429,212,57,-426,810,

%U -810,407,113,-801,1479,-1478,759,208,-1457,2640,-2637,1371,381,-2589,4598,-4590,2419,669

%N Expansion of 1 / Sum_{k in Z} x^k / (1 - x^(5*k+2)).

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

%o (PARI) my(N=60, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^k/(1-x^(5*k+2))))

%o (PARI) my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(5*k-1))*(1-x^(5*k-4))/(1-x^(5*k))^2))

%Y Convolution inverse of A340453.

%Y Cf. A375061, A375062, A375064.

%K sign

%O 0,6

%A _Seiichi Manyama_, Jul 29 2024