A189049 Denominators of expansion of (Sum_{k=1..n} 1/k) - log(n(1+1/(2n))) - gamma.

24, 24, 960, 160, 8064, 896, 30720, 4608, 337920, 22528, 67092480, 106496, 688128, 491520, 267386880, 2228224, 1882718208, 9961472, 3460300800, 44040192, 6366953472, 192937984, 549621596160, 838860800

Offset

2,1

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]] // Denominator (* Jean-François Alcover, Sep 12 2013 *)

Crossrefs

Cf. A189048.

Sequence in context: A056455 A128378 A165845 * A239153 A371971 A004513

Adjacent sequences: A189046 A189047 A189048 * A189050 A189051 A189052

Keyword

nonn,frac,more

Author

N. J. A. Sloane, Apr 16 2011

Extensions

More terms from Jean-François Alcover, Sep 12 2013

Status

approved