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%I #8 Sep 22 2020 20:23:38
%S 1,4,4,169,555025,14291007025,8480906296345283491681,
%T 3964171123687651228091479334301620432503354561,
%U 1124604806436444518574523753367158577376786150279857801748598100182341756509785760684694337921
%N Numerator of f(n) where f(1) = 1, f(n+1) = n^2/f(n) + f(n)/n^2 + 2.
%H Y. Chen and others, <a href="http://www.jstor.org/stable/4145179">Variation of a Ukrainian Olympiad Problem: Problem 10982</a>, Amer. Math. Monthly, 111 (No. 7, 2004), 631-632.
%F f(n) -> n + 1/2.
%e 1, 4, 4, 169/36, 555025/97344, 14291007025/2161134144, ...
%t nxt[{n_,a_}]:={n+1,n^2/a+a/n^2+2}; NestList[nxt,{1,1},10][[All,2]]//Numerator (* _Harvey P. Dale_, Sep 22 2020 *)
%Y Cf. A097573.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Aug 29 2004