A372386 Decimal expansion of Sum_{k>=0} (k^2+1) / (k^4+1).

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, 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, 3, 4, 0, 3, 6, 6, 5, 2, 2, 2, 2, 4, 6, 0, 0, 4, 2, 3

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Formula

Equals 1/2 - Pi*sinh(sqrt(2)*Pi)/(sqrt(2)*(cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))). - Vaclav Kotesovec, May 14 2024

Example

2.70700550439144692373008082699544766873309901571997...

Mathematica

s = Sum[ (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
d = Chop[N[s, 100]]
First[RealDigits[d]]
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 *)

Crossrefs

Cf. A372387.

Sequence in context: A021791 A378715 A325905 * A199273 A196833 A245224

Adjacent sequences: A372383 A372384 A372385 * A372387 A372388 A372389

Keyword

nonn,cons

Author

Clark Kimberling, May 12 2024

Status

approved