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%I #12 Aug 20 2017 09:22:22
%S 1,-1,1,-1,1,0,-1,2,-3,3,-2,0,3,-6,7,-6,2,5,-12,17,-17,9,6,-24,40,-45,
%T 32,-1,-44,89,-112,97,-34,-72,189,-272,273,-153,-84,380,-637,723,-526,
%U 22,703,-1427,1824,-1593,575,1126,-3041,4423,-4461,2562,1251,-6096
%N Expansion of 1/(1 + x/(1 + x^4/(1 + x^9/(1 + x^16/(1 + x^25/(1 + ... + x^(k^2)/(1 + ...))))))), a continued fraction.
%e G.f.: A(x) = 1 - x + x^2 - x^3 + x^4 - x^6 + 2*x^7 - 3*x^8 + 3*x^9 - 2*x^10 + ...
%t nmax = 55; CoefficientList[Series[1/(1 + ContinuedFractionK[x^k^2, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000290, A007325, A206739.
%K sign
%O 0,8
%A _Ilya Gutkovskiy_, Apr 18 2017
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