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%I #12 May 18 2024 15:09:38
%S 2,7,0,7,0,0,5,5,0,4,3,9,1,4,4,6,9,2,3,7,3,0,0,8,0,8,2,6,9,9,5,4,4,7,
%T 6,6,8,7,3,3,0,9,9,0,1,5,7,1,9,9,7,3,1,6,2,5,4,4,1,2,0,5,8,8,0,4,9,9,
%U 3,4,0,3,6,6,5,2,2,2,2,4,6,0,0,4,2,3
%N Decimal expansion of Sum_{k>=0} (k^2+1) / (k^4+1).
%F Equals 1/2 - Pi*sinh(sqrt(2)*Pi)/(sqrt(2)*(cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))). - _Vaclav Kotesovec_, May 14 2024
%e 2.70700550439144692373008082699544766873309901571997...
%t s = Sum[ (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
%t d = Chop[N[s, 100]]
%t First[RealDigits[d]]
%t RealDigits[1/2 - Pi*Sinh[Sqrt[2]*Pi]/(Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 120][[1]] (* _Vaclav Kotesovec_, May 14 2024 *)
%Y Cf. A372387.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, May 12 2024
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