A012960 - OEIS

%I #12 May 10 2020 13:42:48

%S 1,2,3,2,-11,-30,175,1010,-6135,-60670,374875,5719650,-35199875,

%T -779710750,4687746375,145208599250,-836951243375,-35435177514750,

%U 191995883837875,10975003189933250,-54688433347786875

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

%F a(n) = (n*A002019(n)-A002019(n+1))/(n-1) for n > 1. [_Mark van Hoeij_, Jul 02 2010]

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

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

%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(atan(x)+log(x+1)))) \\ _Michel Marcus_, May 10 2020

%Y Cf. A002019.

%K sign

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, Jul 25 2013