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

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..92.

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

Formula

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

Example

0.125567284722879676...

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 *)

Crossrefs

Cf. A002163, A002390, A145433.

Sequence in context: A130851 A130856 A004095 * A220426 A117899 A120839

Adjacent sequences: A145431 A145432 A145433 * A145435 A145436 A145437

Keyword

cons,easy,nonn

Author

R. J. Mathar, Feb 08 2009

Status

approved