A013254 Expansion of e.g.f. arctanh(log(x+1) - arctan(x)).

0, 0, -1, 4, -6, 0, -150, 2280, -16520, 96320, -1053360, 17870400, -264765600, 3541824000, -51903131280, 904820280000, -17470217232000, 351612581299200, -7290584110742400, 157383219788121600

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Example

-(1/2!)*x^2 + (4/3!)*x^3 - (6/4!)*x^4 - (150/6!)*x^6 + ...

Mathematica

With[{nn=20}, Drop[CoefficientList[Series[ArcTanh[Log[x+1]-ArcTan[x]], {x, 0, nn}], x] Range[0, nn]!, 2]] (* Harvey P. Dale, Sep 30 2016 *)

Prog

(PARI) x = 'x + O('x^30); concat([0, 0], Vec(serlaplace(atanh(log(x+1) - atan(x))))) \\ Michel Marcus, Aug 03 2018

Crossrefs

Sequence in context: A013251 A013247 A013248 * A094920 A010668 A200601

Adjacent sequences: A013251 A013252 A013253 * A013255 A013256 A013257

Keyword

sign

Author

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

Extensions

Definition edited by Harvey P. Dale, Sep 30 2016

a(0)=a(1)=0 inserted and title improved by Sean A. Irvine, Aug 02 2018

Status

approved