A013570 Numerator of [x^n] of the Taylor series log(arctan(x)/log(x+1)).

1, -13, 1, 11, 19, -10243, 751, 49873, 2857, -72752269, 434293, 1524997, 8181904909, -454156185199, 5044289, 23214243090113, 5026792806787, -2652186577877894731, 69028763155644023

Offset

1,2

Comments

The inner function is arctan(x)/log(x+1) = 1 + x/2 - 5*x^2/12 - x^3/8 + 29*x^4/144 + 151*x^5/1440 - 9979*x^6/60480 - ...

Links

G. C. Greubel, Table of n, a(n) for n = 1..400

Example

Log(arctan(x)/log(x+1)) = x/2 - 13*x^2/24 + x^3/8 + 11*x^4/192 + 19*x^5/288 - 10243*x^6/72576 + ...

Mathematica

Numerator[Take[CoefficientList[Series[Log[ArcTan[x]/Log[x + 1]], {x, 0, 50}], x], {1, -1, 1}]] (* G. C. Greubel, Nov 19 2016 *)

Crossrefs

Sequence in context: A185409 A010235 A196381 * A010236 A058018 A037283

Adjacent sequences: A013567 A013568 A013569 * A013571 A013572 A013573

Keyword

sign,frac

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Name edited by R. J. Mathar, Dec 22 2011

Status

approved