A189048 - OEIS

%I #14 Dec 26 2023 10:04:08

%S 1,-1,23,-1,-11,-1,143,-1,-2527,-1,1416533,-1,-57341,-1,118522111,-1,

%T -5749735025,-1,91546452133,-1,-1792043646907,-1,1982765704676693,-1

%N Numerators of expansion of (Sum_{k=1..n} 1/k) - log(n(1+1/(2n))) - gamma.

%H E. Chlebus, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.118.03.268">A recursive scheme for improving the original rate of convergence to the Euler-Mascheroni constant</a>, Amer. Math. Mnthly, 118 (2011), 268-274.

%e 1/(24n^2) - 1/(24n^3) + 23/(960*n^4) - 1/(160n^5) - 11/(8064*n^6) - 1/(896n^7) + 143/(30720*n^8) + ...

%t s = Sum[1/k, {k, 1, n}] - Log[n*(1 + 1/(2*n))] - EulerGamma; CoefficientList[ Series[s, {n, Infinity, 25}], 1/n][[3 ;; -1]] // Numerator (* _Jean-François Alcover_, Sep 12 2013 *)

%Y Cf. A189049.

%K sign,frac,more

%O 2,3

%A _N. J. A. Sloane_, Apr 16 2011

%E Corrected and extended by _Jean-François Alcover_, Sep 12 2013