A157701 Decimal expansion of 2*(14*sigma+5)/625 where sigma = sqrt(5)*log(golden ratio).

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

Offset: 0

Author

R. J. Mathar, Mar 04 2009

Keywords

• cons
• easy
• nonn

Comments

The factor 28 in the Lehmer paper has been corrected to 14.

Equals sum_{n=1..infinity} (-1)^n*n^3/binomial(2n,n).

Examples

			0.064205801387968452355..
		

Links

• D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.
• R. J. Mathar, Corrigenda to "Interesting series involving...", arXiv:0905.0215
• Index entries for transcendental numbers

Crossrefs

Cf. A145434, A145433.

Programs

Maple

2/625*(14*sqrt(5)*log((1+sqrt(5))/2)+5) ;

Mathematica

Join[{0},RealDigits[2*(14*Sqrt[5]*Log[GoldenRatio]+5)/625,10,120][[1]]] (* Harvey P. Dale, Mar 13 2015 *)

PARI

2*(14*sqrt(5)*log((sqrt(5)+1)/2)+5)/625 \\ Charles R Greathouse IV, May 15 2019

Formula

Equals 2*(14*A002163*A002390+5)/625 .