A145434 Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n^2/binomial(2n,n).

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

Offset: 0

Author

R. J. Mathar, Feb 08 2009

Keywords

• cons
• easy
• nonn

Comments

The numerator in the Apelblat table lacks the square (typo).

Examples

			0.125567284722879676...
		

References

• Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.40.

Links

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

Crossrefs

Cf. A002163, A002390, A145433.

Programs

Maple

evalf( 4/25-4/125*5^(1/2)*log(1/2+1/2*5^(1/2)), 120) ;

Mathematica

RealDigits[HypergeometricPFQ[{2, 2, 2}, {1, 3/2}, -1/4]/2, 10, 93] // First
(* or *) RealDigits[4/25 - 4*Sqrt[5]*Log[GoldenRatio]/125, 10, 93] // First (* Jean-François Alcover, Feb 13 2013, updated Oct 27 2014 *)

Formula

Equals 4*(5-A002163*A002390)/125.