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%I #9 Mar 28 2015 21:59:27
%S 2,0,2,5,4,3,8,4,6,7,7,7,6,5,7,3,8,8,7,7,1,3,5,1,8,7,3,9,1,4,1,7,6,5,
%T 2,4,7,0,6,5,2,9,3,0,6,1,7,6,5,8,2,8,3,9,5,5,6,2,9,2,4,7,5,5,2,6,2,3,
%U 2,4,2,5,0,9,6,3,2,5,4,7,3,7,9,1,9,3,2,2,0,8,4,1,6,5,3,8,6,5,9,6,8,6,4,7,5
%N Fill's second logarithmic constant.
%H J. A. Fill, Ph. Flajolet and N. Kapur, <a href="http://arXiv.org/abs/math.CO/0306225">Singularity analysis, Hadamard products and tree recurrences</a>
%F Sum[k>=1, log(k)/{(k+1)*4^k} * C(2n, n)].
%F -gamma-Integral_{0..1}, log(log(1/t))/{ sqrt(1-t)(1+sqrt(1-t))2 } dt. - _Robert G. Wilson v_, Aug 24 2004
%e 2.0254384677765738877...
%t $MaxExtraPrecision = 256; $MaxPrecision = 2560000; k = NIntegrate[ Log[ Log[1/t]]/(Sqrt[1 - t](1 + Sqrt[1 - t])^2), {t, 0, 1}, AccuracyGoal -> 80, WorkingPrecision -> 128, MaxRecursion -> 32]; RealDigits[ N[ -EulerGamma - k, 105]][[1]] (* _Robert G. Wilson v_, Aug 24 2004 *)
%Y Cf. A094720.
%K nonn,cons
%O 1,1
%A _Ralf Stephan_, May 25 2004
%E More terms from _Robert G. Wilson v_, Aug 24 2004
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