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 A372387 #11 May 18 2024 15:09:50
%S A372387 2,1,3,4,1,5,4,5,7,1,0,8,7,5,7,8,3,3,2,0,8,8,4,0,0,4,0,8,9,6,6,3,6,4,
%T A372387 2,1,2,0,4,7,1,3,2,7,0,5,3,1,0,1,4,4,6,5,9,8,1,4,5,6,1,0,1,0,3,0,9,5,
%U A372387 8,4,8,3,1,8,2,0,5,0,6,7,1,2,3,8,2,4
%N A372387 Decimal expansion of Sum_{k>=0} (-1)^k*(k^2+1) / (k^4+1).
%F A372387 Equals 1/2 + sqrt(2)*Pi*cos(Pi/sqrt(2))*sinh(Pi/sqrt(2))/(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi)). - _Vaclav Kotesovec_, May 14 2024
%e A372387 0.2134154571087578332088400408966364212047132705...
%t A372387 s = Sum[(-1)^k * (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
%t A372387 d = Chop[N[s, 100]]
%t A372387 First[RealDigits[d]]
%t A372387 RealDigits[1/2 + Sqrt[2]*Pi*Cos[Pi/Sqrt[2]]*Sinh[Pi/Sqrt[2]] / (Cosh[Sqrt[2]*Pi] - Cos[Sqrt[2]*Pi]), 10, 120][[1]] (* _Vaclav Kotesovec_, May 14 2024 *)
%o A372387 (PARI) sumalt(k=0, (-1)^k*(k^2+1)/(k^4+1)) \\ _Michel Marcus_, May 15 2024
%Y A372387 Cf. A372386.
%K A372387 nonn,cons
%O A372387 0,1
%A A372387 _Clark Kimberling_, May 12 2024