A229703 Decimal expansion of Sum_{k>=1} (-1)^k/(k*binomial(4k,k)) (negated).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Necdet Batir and Anthony Sofo, On some series involving reciprocals of binomial coefficients, Appl. Math. Comp. 220 (2013) 331-338, Example 6.

Formula

Equals (3*d/(2*d^2+1))*log(abs((d-1)/(d+1))) + (3*(d-1)/(2*(2*d^2+1))) * sqrt(d/(d+2)) * arctan(2*sqrt(d^2+2*d)/(d^2+2*d-1)) - (3*(d+1)/(2*(2*d^2+1))) * sqrt(d/(d-2)) * arctan(2*sqrt(d^2-2*d)/(d^2-2*d-1)), where d = sqrt(1 - (8/sqrt(3))*(((3*sqrt(3)+sqrt(283))/16)^(1/3) - (((3*sqrt(3)+sqrt(283))/16)^(-1/3)))) (Batir and Sofo, 2013). - Amiram Eldar, Dec 07 2024

Example

-0.2335324174851719887871681394896038...

Mathematica

HypergeometricPFQ[{1, 1, 4/3, 5/3}, {5/4, 3/2, 7/4}, -27/256]/4 // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 18 2014 *)

Crossrefs

Cf. A225847, A378802.

Sequence in context: A232932 A252502 A063256 * A348883 A131320 A020483

Adjacent sequences: A229700 A229701 A229702 * A229704 A229705 A229706

Keyword

nonn,cons

Author

R. J. Mathar, Sep 27 2013

Status

approved