A229704 Decimal expansion of Sum_{k>=1} (-1)^k/(k*binomial(3k,k)) (negated).

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

Offset

0,1

Links

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

Jonathan M. Borwein and Roland Girgensohn, Evaluations of binomial series, aequationes mathematicae, Vol. 70, No. 1 (2005), pp. 25-36. See p. 35, eq. (61).

Formula

Equals -log(2) + Sum_{r: r^3 + 4*r + 8 = 0} log(r+2)/(r+3) (Borwein and Girgensohn, 2005). - Amiram Eldar, Dec 07 2024

Example

-0.3035219049723491543737906347..

Mathematica

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

Crossrefs

Cf. A005809.

Sequence in context: A127749 A198431 A138188 * A372865 A380343 A014715

Adjacent sequences: A229701 A229702 A229703 * A229705 A229706 A229707

Keyword

nonn,cons

Author

R. J. Mathar, Sep 27 2013

Status

approved