This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229703 #19 Dec 08 2024 02:34:37
%S A229703 2,3,3,5,3,2,4,1,7,4,8,5,1,7,1,9,8,8,7,8,7,1,6,8,1,3,9,4,8,9,6,0,3,8,
%T A229703 2,1,7,5,6,9,1,1,2,1,6,0,1,9,6,6,6,2,5,1,8,0,6,2,4,3,5,4,3,5,9,9,3,9,
%U A229703 3,1,3,9,2,4,3,5,4,6,7,7,8,9,0,6,4,1,1,8,6,4,7,6,3,4,4,3,8,5,7,6,4,7,7,2,4
%N A229703 Decimal expansion of Sum_{k>=1} (-1)^k/(k*binomial(4k,k)) (negated).
%H A229703 Necdet Batir and Anthony Sofo, <a href="http://dx.doi.org/10.1016/j.amc.2013.05.053">On some series involving reciprocals of binomial coefficients</a>, Appl. Math. Comp. 220 (2013) 331-338, Example 6.
%F A229703 Equals (3*d/(2*d^2+1))*log(abs((d-1)/(d+1))) + (3*(d-1)/(2*(2*d^2+1))) * sqrt(d/(d+2)) * arctan(2*sqrt(d^2+2*d)/(d^2+2*d-1)) - (3*(d+1)/(2*(2*d^2+1))) * sqrt(d/(d-2)) * arctan(2*sqrt(d^2-2*d)/(d^2-2*d-1)), where d = sqrt(1 - (8/sqrt(3))*(((3*sqrt(3)+sqrt(283))/16)^(1/3) - (((3*sqrt(3)+sqrt(283))/16)^(-1/3)))) (Batir and Sofo, 2013). - _Amiram Eldar_, Dec 07 2024
%e A229703 -0.2335324174851719887871681394896038...
%t A229703 HypergeometricPFQ[{1, 1, 4/3, 5/3}, {5/4, 3/2, 7/4}, -27/256]/4 // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A229703 Cf. A225847, A378802.
%K A229703 nonn,cons
%O A229703 0,1
%A A229703 _R. J. Mathar_, Sep 27 2013