A012960 Expansion of e.g.f. exp(arctan(x)+log(x+1)).

1, 2, 3, 2, -11, -30, 175, 1010, -6135, -60670, 374875, 5719650, -35199875, -779710750, 4687746375, 145208599250, -836951243375, -35435177514750, 191995883837875, 10975003189933250, -54688433347786875

Offset: 0

Author

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

Keywords

• sign

Examples

			1+2*x+3/2!*x^2+2/3!*x^3-11/4!*x^4-30/5!*x^5...
		

Crossrefs

Cf. A002019.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcTan[x]+Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 25 2013 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(atan(x)+log(x+1)))) \\ Michel Marcus, May 10 2020

Formula

a(n) = (n*A002019(n)-A002019(n+1))/(n-1) for n > 1. [Mark van Hoeij, Jul 02 2010]

Extensions

Definition clarified by Harvey P. Dale, Jul 25 2013