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The denominator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.
1

%I #17 Jul 15 2017 11:22:32

%S 2,2,2,2,10,90,4410,2033010,47753371890,536047310324601810,

%T 146146505822254040921594435610,

%U 461461505298297622704608601547181743257756610890,409066116871912908631970281597531260628466742447938742767153852110729821286410

%N The denominator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.

%C It appears that the sequence is always in simplest terms when generated.

%t r[n_] := r[n] = If[n <= 2, 1/2, 1/r[n - 2] + r[n - 1]]; Denominator@ Array[r, 13] (* _Michael De Vlieger_, Jul 15 2017 *)

%Y Cf. A289909 (numerators).

%K nonn,frac

%O 1,1

%A _John Harmon_, Jul 15 2017