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 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified September 16 09:24 EDT 2024. Contains 375965 sequences. (Running on oeis4.)