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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.
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%I #4 Sep 25 2017 13:08:18

%S 1,0,1,1,1,2,2,3,5,5,10,11,17,25,31,50,64,93,134,178,266,360,512,731,

%T 1001,1447,2003,2829,4011,5575,7939,11097,15634,22085,30909,43724,

%U 61369,86389,121810,171007,241216,339125,477292,672364,945252,1331677,1873473,2636704,3712653

%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 = 48; 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, A088352, A285407, A292800, A292801.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Sep 23 2017