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G.f.: 1/(1 + x/(1 + 2*x^2/(1 + 3*x^3/(1 + 4*x^4/(1 + 5*x^5/(1 + 6*x^6/(1 + ... ))))))), a continued fraction.
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%I #4 Apr 18 2017 15:38:08

%S 1,-1,1,1,-3,1,-1,5,3,-13,19,-41,9,55,-55,113,-99,65,-113,-491,843,

%T -245,-325,1295,-783,-121,-887,-287,2685,-6911,7559,12413,-36669,

%U 12179,42211,-59681,55281,-22313,38633,19361,-465579,877913,-711185,-575339,2540955,-3065165,1681907,-29953,-1287375,7293527,-19374047

%N G.f.: 1/(1 + x/(1 + 2*x^2/(1 + 3*x^3/(1 + 4*x^4/(1 + 5*x^5/(1 + 6*x^6/(1 + ... ))))))), a continued fraction.

%e G.f.: A(x) = 1 - x + x^2 + x^3 - 3*x^4 + x^5 - x^6 + 5*x^7 + 3*x^8 - 13*x^9 + ...

%t nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[k x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A007325, A088357.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Apr 18 2017