A189048 Numerators of expansion of (Sum_{k=1..n} 1/k) - log(n(1+1/(2n))) - gamma.

1, -1, 23, -1, -11, -1, 143, -1, -2527, -1, 1416533, -1, -57341, -1, 118522111, -1, -5749735025, -1, 91546452133, -1, -1792043646907, -1, 1982765704676693, -1

Offset

2,3

Links

Table of n, a(n) for n=2..25.

E. Chlebus, A recursive scheme for improving the original rate of convergence to the Euler-Mascheroni constant, Amer. Math. Mnthly, 118 (2011), 268-274.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A189049.

Sequence in context: A040546 A040547 A040548 * A040549 A069890 A040550

Adjacent sequences: A189045 A189046 A189047 * A189049 A189050 A189051

Keyword

sign,frac,more

Author

N. J. A. Sloane, Apr 16 2011

Extensions

Corrected and extended by Jean-François Alcover, Sep 12 2013

Status

approved