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A270859 Decimal expansion of Sum_{n >= 1} |G_n|/n^2, where G_n are Gregory's coefficients. 3
5, 2, 9, 0, 5, 2, 9, 6, 9, 9, 4, 0, 4, 3, 9, 0, 2, 4, 0, 7, 2, 2, 9, 3, 9, 3, 9, 4, 7, 5, 5, 8, 9, 7, 2, 8, 0, 9, 4, 0, 3, 8, 1, 7, 1, 6, 9, 5, 9, 6, 2, 5, 6, 9, 0, 8, 6, 1, 7, 1, 8, 2, 8, 0, 9, 7, 2, 7, 7, 7, 2, 2, 9, 6, 8, 5, 1, 1, 3, 4, 8, 0, 0, 6, 5, 2, 0, 7, 2, 8, 9, 1, 1, 3, 2, 5, 5, 9, 9, 6, 4, 0, 9, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Gregory's coefficients (A002206 and A002207) are also knwon 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

Table of n, a(n) for n=0..103.

Iaroslav V. Blagouchine and Marc-Antoine Coppo, A note on some constants related to the zeta-function and their relationship with the Gregory coefficients, arXiv:1703.08601 [math.NT], 2017.

FORMULA

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

EXAMPLE

0.5290529699404390240722939394755897280940381716959625...

MAPLE

evalf(int((-Li(1-x)+gamma+ln(x))/x, x = 0..1), 150)

MATHEMATICA

N[Integrate[(-LogIntegral[1 - x] + EulerGamma + Log[x])/x, {x, 0, 1}], 150]

CROSSREFS

Cf. A270857, A269330, A001620, A002206, A002207, A195189.

Sequence in context: A046878 A078335 A021658 * A248749 A248751 A021193

Adjacent sequences:  A270856 A270857 A270858 * A270860 A270861 A270862

KEYWORD

nonn,cons

AUTHOR

Iaroslav V. Blagouchine, Mar 24 2016

STATUS

approved

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Last modified October 22 17:42 EDT 2018. Contains 316498 sequences. (Running on oeis4.)