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%I #14 Sep 25 2017 13:05:07
%S 1,1,2,6,14,34,194,1282,1462,18218,146086,1457782,6716878,39074098,
%T 45252802,5408759762,31474373714,234791957218,603801637054,
%U 9995479925774,3351221125294,639914357324914,9795281594021882,194090616503597114,1604611166042748122
%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 numerator 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) = 1.
%e b(2) = 1/(1+1^2/(1+1^2)) = 2/3, so a(2) = 2.
%e b(3) = 1/(1+1^2/(1+1^2/(1+2^2))) = 6/11, so a(3) = 6.
%e b(4) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2)))) = 14/23, so a(4) = 14.
%Y Cf. A091659, A292817.
%K nonn,frac
%O 0,3
%A _Seiichi Manyama_, Sep 24 2017
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