This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372386 #12 May 18 2024 15:09:38
%S A372386 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 A372386 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 A372386 3,4,0,3,6,6,5,2,2,2,2,4,6,0,0,4,2,3
%N A372386 Decimal expansion of Sum_{k>=0} (k^2+1) / (k^4+1).
%F A372386 Equals 1/2 - Pi*sinh(sqrt(2)*Pi)/(sqrt(2)*(cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))). - _Vaclav Kotesovec_, May 14 2024
%e A372386 2.70700550439144692373008082699544766873309901571997...
%t A372386 s = Sum[ (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
%t A372386 d = Chop[N[s, 100]]
%t A372386 First[RealDigits[d]]
%t A372386 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 A372386 Cf. A372387.
%K A372386 nonn,cons
%O A372386 1,1
%A A372386 _Clark Kimberling_, May 12 2024