A367976 Decimal expansion of Sum_{k >= 0} (-1)^k/(1+k^2).

6, 3, 6, 0, 1, 4, 5, 2, 7, 4, 9, 1, 0, 6, 6, 5, 8, 1, 4, 7, 5, 1, 1, 8, 2, 9, 1, 8, 3, 6, 0, 1, 8, 7, 7, 7, 9, 2, 0, 3, 5, 9, 1, 8, 1, 7, 3, 0, 1, 5, 7, 9, 7, 4, 7, 5, 3, 4, 4, 8, 3, 9, 1, 9, 2, 8, 1, 2, 3, 0, 9, 5, 6, 8, 4, 7, 4, 3, 9, 4, 4, 0, 9, 5, 5, 7, 6, 5, 5, 8, 6, 0, 5, 3, 4, 6, 8, 8, 2, 2, 4, 3, 0, 5

Offset

0,1

Links

Table of n, a(n) for n=0..103.

Formula

Equals (2-Pi*tanh(Pi/2)+Pi*coth(Pi/2))/4 = (1 - A228048 + Pi/2*A367961)/2.

From Amiram Eldar, Dec 11 2023: (Start)

Equals (1 + Pi/sinh(Pi))/2.

Equals Integral_{x>=0} (cos(x)/cosh(x))^2 dx. (End)

Equals (1+A090986)/2. - R. J. Mathar, Dec 13 2023

Example

0.636014527491066581475118291836...

Maple

1/4*(2-Pi*tanh(Pi/2)+Pi*coth(Pi/2)) ; evalf(%) ;

Mathematica

RealDigits[(1 + Pi*Csch[Pi])/2, 10, 120][[1]] (* Amiram Eldar, Dec 11 2023 *)

Prog

(PARI) sumalt(k=0, (-1)^k/(1+k^2)) \\ Michel Marcus, Dec 07 2023
(PARI) sumnumrat((4*n + 1)/(16*n^4 + 16*n^3 + 12*n^2 + 4*n + 2), 0) \\ Charles R Greathouse IV, May 18 2026
(PARI) (Pi/sinh(Pi)+1)/2 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A113319.

Sequence in context: A319894 A241786 A019151 * A143506 A248580 A008567

Adjacent sequences: A367973 A367974 A367975 * A367977 A367978 A367979

Keyword

nonn,cons

Author

R. J. Mathar, Dec 07 2023

Status

approved