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A094721 Fill's second logarithmic constant. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A078182 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

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Last modified November 20 20:57 EST 2018. Contains 317422 sequences. (Running on oeis4.)