A145433 Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n/binomial(2n,n).

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

Offset: 0

Author

R. J. Mathar, Feb 08 2009

Keywords

• cons
• easy
• nonn

Examples

			0.274432715277120323...
		

References

• Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.39

Links

• Steven Finch, Central Binomial Coefficients [Cached copy, with permission of the author]

Crossrefs

Cf. A002163, A002390, A145434.

Programs

Maple

6/25+4/125*5^(1/2)*ln(1/2+1/2*5^(1/2)) ;

Mathematica

RealDigits[6/25 + 4*Sqrt[5]*Log[GoldenRatio]/125, 10, 93] // First (* Jean-François Alcover, Oct 27 2014 *)
RealDigits[Hypergeometric2F1[2, 2, 3/2, -1/4]/2, 10, 93] // First (* Vaclav Kotesovec, Oct 27 2014 *)

Formula

Equals 2*(15+2*A002163*A002390)/125.