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A094691
Decimal expansion of -Integral_{x=0..1} (sqrt(x)/log(1-x)) dx.
1
1, 6, 0, 1, 4, 0, 2, 2, 4, 3, 5, 4, 9, 8, 8, 7, 6, 1, 3, 9, 3, 3, 2, 4, 9, 8, 9, 2, 3, 7, 1, 2, 8, 6, 0, 5, 6, 6, 7, 2, 4, 1, 0, 8, 9, 9, 3, 1, 4, 1, 6, 5, 4, 5, 3, 2, 7, 3, 1, 1, 4, 8, 7, 1, 0, 4, 5, 7, 3, 8, 5, 5, 4, 8, 3, 8, 7, 5, 0, 4, 5, 8, 8, 3, 7, 9, 3, 0, 6, 8
OFFSET
1,2
FORMULA
Equals 5/3 - 2*Sum_(abs(Sum_((BernoulliB(j)*Stirling1(k, j-1))/j, {j, 1, k+1}))/((2*k+3)*k!), k=1..infinity}). [Jean-François Alcover, Apr 12 2013]
Equals Integral_{x=0..1} beta(x+1,1/2) dx. - Jean-Luc Marichal, Sep 22 2020
EXAMPLE
1.601402243549887613933249892371286056672410899314165453273114871045738554838...
MATHEMATICA
-NIntegrate[ Sqrt[x]/Log[1 - x], {x, 0, 1}, MaxRecursion -> 24, WorkingPrecision -> 98]
RealDigits[NIntegrate[Sqrt[x]/Log[1-x], {x, 0, 1}, WorkingPrecision-> 120], 10, 120] [[1]] (* Harvey P. Dale, Apr 05 2019 *)
PROG
(PARI) -intnum(x=0, 1, sqrt(x)/log(1-x)) \\ Michel Marcus, Sep 23 2020
CROSSREFS
Sequence in context: A011253 A049248 A178601 * A095715 A321215 A141108
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, May 19 2004
EXTENSIONS
Corrected and extended by Harvey P. Dale, Apr 05 2019
STATUS
approved