A372387 Decimal expansion of Sum_{k>=0} (-1)^k*(k^2+1) / (k^4+1).

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, 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, 8, 4, 8, 3, 1, 8, 2, 0, 5, 0, 6, 7, 1, 2, 3, 8, 2, 4

Offset: 0

Author

Clark Kimberling, May 12 2024

Keywords

• nonn
• cons

Examples

			0.2134154571087578332088400408966364212047132705...
		

Crossrefs

Cf. A372386.

Programs

Mathematica

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

PARI

sumalt(k=0, (-1)^k*(k^2+1)/(k^4+1)) \\ Michel Marcus, May 15 2024

Formula

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