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%I #9 Jun 07 2024 14:16:21
%S 1,14,13,14,31,86,19,146,91,74,133,314,61,422,241,182,307,686,127,842,
%T 463,338,553,1202,217,1406,757,542,871,1862,331,2114,1123,794,1261,
%U 2666,469,2966,1561,1094,1723,3614,631,3962,2071,1442,2257,4706,817,5102
%N a(n) = denominator of Sum_{k>=0} cos(k*Pi/3)/n^k.
%C The first five fractions are 1/1, 15/14, 14/13, 15/14, 33/31; beginning at 14/13 the sequence of fractions is strictly decreasing with limit 1.
%t t = Table[Sum[Cos[k Pi/3]/n^k, {k, 0, Infinity}], {n, 2, 60}]
%t Denominator[t]
%t (* or *)
%t Denominator[Table[(n*(2*n - 1))/(2*(n^2 - n + 1)), {n, 2, 100}]] (* _Vaclav Kotesovec_, May 28 2024 *)
%Y Cf. A373161, A373162, A373163.
%K nonn,frac
%O 2,2
%A _Clark Kimberling_, May 28 2024
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