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%I #30 Feb 24 2022 07:27:34
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n^2/binomial(2n,n).
%C The numerator in the Apelblat table lacks the square (typo).
%D Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.40.
%H Steven Finch, <a href="/A145433/a145433.pdf">Central Binomial Coefficients</a> [Cached copy, with permission of the author]
%F Equals 4*(5-A002163*A002390)/125.
%e 0.125567284722879676...
%p evalf( 4/25-4/125*5^(1/2)*log(1/2+1/2*5^(1/2)), 120) ;
%t RealDigits[HypergeometricPFQ[{2, 2, 2}, {1, 3/2}, -1/4]/2, 10, 93] // First
%t (* or *) RealDigits[4/25 - 4*Sqrt[5]*Log[GoldenRatio]/125, 10, 93] // First (* _Jean-François Alcover_, Feb 13 2013, updated Oct 27 2014 *)
%Y Cf. A002163, A002390, A145433.
%K cons,easy,nonn
%O 0,2
%A _R. J. Mathar_, Feb 08 2009