A270857 Decimal expansion of Sum_{n >= 1} G_n/n^2, where G_n are Gregory's coefficients.

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

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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)-gamma-ln(x))/x, x = 0..1), 120);

Mathematica

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

Crossrefs

Cf. A270859, A269330, A001620, A002206, A002207, A195189.

Sequence in context: A059627 A200603 A159591 * A113307 A021901 A159194

Adjacent sequences: A270854 A270855 A270856 * A270858 A270859 A270860

Keyword

nonn,cons

Author

Iaroslav V. Blagouchine, Mar 24 2016

Extensions

Mathematica program corrected by Harvey P. Dale, Jul 05 2022

Status

approved