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%I #20 Jun 02 2017 00:38:02
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n/binomial(2n,n).
%D Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.39
%H Steven Finch, <a href="/A145433/a145433.pdf">Central Binomial Coefficients</a> [Cached copy, with permission of the author]
%F Equals 2*(15+2*A002163*A002390)/125.
%e 0.274432715277120323...
%p 6/25+4/125*5^(1/2)*ln(1/2+1/2*5^(1/2)) ;
%t RealDigits[6/25 + 4*Sqrt[5]*Log[GoldenRatio]/125, 10, 93] // First (* _Jean-François Alcover_, Oct 27 2014 *)
%t RealDigits[Hypergeometric2F1[2, 2, 3/2, -1/4]/2, 10, 93] // First (* _Vaclav Kotesovec_, Oct 27 2014 *)
%Y Cf. A002163, A002390, A145434.
%K cons,easy,nonn
%O 0,1
%A _R. J. Mathar_, Feb 08 2009
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