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%I #14 Dec 08 2024 02:34:58
%S 3,0,3,5,2,1,9,0,4,9,7,2,3,4,9,1,5,4,3,7,3,7,9,0,6,3,4,7,2,9,4,7,9,6,
%T 0,1,8,8,6,2,4,7,3,9,4,2,1,6,6,7,1,3,7,8,4,3,0,3,0,6,4,2,5,3,1,8,6,9,
%U 1,7,3,5,0,6,8,2,4,3,6,5,4,1,0,1,3,1,1,5,0,1,1,7,4,2,1,7,9,2,1,6,0,3,1,3,2
%N Decimal expansion of Sum_{k>=1} (-1)^k/(k*binomial(3k,k)) (negated).
%H Jonathan M. Borwein and Roland Girgensohn, <a href="https://doi.org/10.1007/s00010-005-2774-x">Evaluations of binomial series</a>, aequationes mathematicae, Vol. 70, No. 1 (2005), pp. 25-36. See p. 35, eq. (61).
%F Equals -log(2) + Sum_{r: r^3 + 4*r + 8 = 0} log(r+2)/(r+3) (Borwein and Girgensohn, 2005). - _Amiram Eldar_, Dec 07 2024
%e -0.3035219049723491543737906347..
%t HypergeometricPFQ[{1, 1, 3/2}, {4/3, 5/3}, -(4/27)]/3 // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y Cf. A005809.
%K nonn,cons
%O 0,1
%A _R. J. Mathar_, Sep 27 2013