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%I #7 Sep 25 2017 13:08:11
%S 1,0,-1,-1,1,2,0,-3,-1,3,4,-3,-7,-1,11,6,-10,-17,8,26,8,-40,-28,33,71,
%T -19,-99,-49,141,125,-99,-285,30,371,253,-492,-541,263,1122,57,-1352,
%U -1197,1672,2260,-548,-4345,-871,4804,5387,-5475,-9182,294,16526,5725,-16587,-23366
%N Expansion of 1/(1 + x^2 + x^3/(1 + x^5 + x^7/(1 + x^11 + x^13/(1 + ... + x^prime(2*k)/(1 + x^prime(2*k+1) + ...))))), a continued fraction.
%t nmax = 55; CoefficientList[Series[1/(1 + x^2 + ContinuedFractionK[x^Prime[2 k], 1 + x^Prime[2 k + 1], {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000040, A092869, A111374, A285407, A292802, A292803.
%K sign
%O 0,6
%A _Ilya Gutkovskiy_, Sep 23 2017