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 A075830 Let u(1)=x, u(n+1)=(n^2/u(n))+1; then u(n)=(b(n)*x+c(n))/(a(n)*x+d(n)). 5

%I

%S 0,1,1,5,7,47,37,319,533,1879,1627,20417,18107,263111,237371,52279,

%T 95549,1768477,1632341,33464927,155685007,166770367,156188887,

%U 3825136961,3602044091,19081066231,18051406831,57128792093,7751493599

%N Let u(1)=x, u(n+1)=(n^2/u(n))+1; then u(n)=(b(n)*x+c(n))/(a(n)*x+d(n)).

%C for x real >0 lim n -> infinity abs(u(n)-n) = (x-1)/(1+(x-1)*log(2)).

%o (PARI) u(n)=if(n<2,x,(n-1)^2/u(n-1)+1); a(n)=polcoeff(denominator(u(n)),1,x)

%Y Apart from leading term, same as A058313.

%Y Cf. A075827, A075828, A075829.

%K nonn

%O 1,4

%A _Benoit Cloitre_, Oct 14 2002

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Last modified June 25 18:30 EDT 2019. Contains 324353 sequences. (Running on oeis4.)