A094721 Fill's second logarithmic constant.

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

J. A. Fill, Ph. Flajolet and N. Kapur, Singularity analysis, Hadamard products and tree recurrences

Formula

Sum[k>=1, log(k)/{(k+1)*4^k} * C(2n, n)].

-gamma-Integral_{0..1}, log(log(1/t))/{ sqrt(1-t)(1+sqrt(1-t))2 } dt. - Robert G. Wilson v, Aug 24 2004

Example

2.0254384677765738877...

Mathematica

$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 *)

Crossrefs

Cf. A094720.

Sequence in context: A363803 A133394 A305628 * A301951 A144529 A319498

Adjacent sequences: A094718 A094719 A094720 * A094722 A094723 A094724

Keyword

nonn,cons

Author

Ralf Stephan, May 25 2004

Extensions

More terms from Robert G. Wilson v, Aug 24 2004

Status

approved