A157700 Decimal expansion of log(4/(1 + sqrt(2))).

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

Offset: 0

Author

R. J. Mathar, Mar 04 2009

Keywords

• cons
• easy
• nonn

Comments

Equals Sum_{n>=2, n even} binomial(2n,n)/(n*4^n) = A016627-A091648.

Examples

			0.5049207741003475936018...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.
• Index entries for transcendental numbers

Programs

Magma

SetDefaultRealField(RealField(100)); Log(4/(1+Sqrt(2))); // G. C. Greubel, Oct 02 2018

Maple

log(4/(1+sqrt(2))) ;

Mathematica

RealDigits[Log[4/(1+Sqrt[2])],10,120][[1]] (* Harvey P. Dale, Jun 08 2014 *)

PARI

default(realprecision, 100); log(4/(1+sqrt(2))) \\ G. C. Greubel, Oct 02 2018