

A270857


Decimal expansion of Sum_{n >= 1} G_n/n^2, where G_n are Gregory's coefficients.


4



4, 8, 2, 6, 4, 4, 2, 2, 1, 6, 2, 0, 4, 6, 2, 6, 1, 2, 3, 7, 9, 4, 2, 8, 3, 9, 1, 1, 4, 8, 5, 7, 5, 7, 7, 3, 9, 7, 0, 1, 2, 0, 3, 9, 6, 2, 7, 5, 6, 6, 5, 6, 7, 0, 5, 0, 2, 3, 0, 1, 6, 5, 1, 6, 2, 9, 5, 1, 5, 8, 0, 9, 1, 0, 7, 1, 8, 2, 0, 0, 9, 7, 6, 2, 4, 3, 0, 1, 7, 9, 5, 1, 1, 6, 5, 3, 4, 3, 0, 1, 5, 3, 7, 3
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OFFSET

0,1


COMMENTS

Gregory's coefficients (A002206 and A002207) are also known as (reciprocal) logarithmic numbers, Bernoulli numbers of the second kind and Cauchy numbers of the first kind. First few coefficients are G_1=+1/2, G_2=1/12, G_3=+1/24, G_4=19/720, etc.


LINKS



FORMULA

Equals integral_{x=0..1} (li(1+x)  gamma  log(x))/x dx, where li(x) is the integral logarithm.


EXAMPLE

0.4826442216204626123794283911485757739701203962756656...


MAPLE

evalf(int((Li(1+x)gammaln(x))/x, x = 0..1), 120);


MATHEMATICA

RealDigits[N[Integrate[(LogIntegral[1+x]EulerGammaLog[x])/x, {x, 0, 1}], 150]][[1]]


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



