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%I #11 Sep 25 2017 13:05:14
%S 1,2,3,11,23,61,329,2281,2515,32285,253195,2577715,11692735,69000385,
%T 78993865,9542994065,55043460305,414012989785,1057309252855,
%U 17617828844255,5873750196655,1127553022142305,17180305293984965,341915575670968805
%N b(0) = 1, b(2*n-1) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+(n-1)^2/(1+n^2)))))) and b(2*n) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+n^2/(1+n^2)))))). a(n) is the denominator of b(n).
%C The limit of b(n) is (PolyGamma(1,(1+sqrt(5))/4)-PolyGamma(1,(3+sqrt(5))/4))/2. See A091659.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanContinuedFractions.html">Ramanujan Continued Fractions</a>
%e b(0) = 1/1, so a(0) = 1.
%e b(1) = 1/(1+1^2) = 1/2, so a(1) = 2.
%e b(2) = 1/(1+1^2/(1+1^2)) = 2/3, so a(2) = 3.
%e b(3) = 1/(1+1^2/(1+1^2/(1+2^2))) = 6/11, so a(3) = 11.
%e b(4) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2)))) = 14/23, so a(4) = 23.
%Y Cf. A091659, A292816.
%K nonn,frac
%O 0,2
%A _Seiichi Manyama_, Sep 24 2017
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