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%I #12 Aug 28 2021 05:38:45
%S 1,7,6,4,0,4,6,8,6,8,7,5,3,2,0,3,4,0,3,8,9,2,8,5,0,0,5,6,3,0,1,0,5,8,
%T 5,6,4,5,5,7,9,1,6,3,7,3,3,8,2,7,5,2,9,1,2,9,3,8,9,8,6,5,7,1,7,8,8,9,
%U 5,3,6,7,5,9,2,5,2,2,3,2,7,1,9,6,3,7
%N Decimal expansion of the limiting ratio of consecutive terms of A289261.
%F Real root of the equation -2 + 2*x - x^2 + 2*x^3 - 2*x^4 + x^5 - 2*x^6 + x^7 = 0. - _Vaclav Kotesovec_, Aug 28 2021
%e 1.7640468687532034038928500563010585645579163733...
%t z = 2000; r = 13/8;
%t u = CoefficientList[Series[1/Sum[Floor[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}], x]; (* A289261 *)
%t v = N[u[[z]]/u[[z - 1]], 200]
%t RealDigits[v, 10][[1]](* A289266 *)
%Y Cf. A078140 (includes guide to related constants), A289261.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Jul 14 2017
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