A012260 - OEIS

%I #14 Sep 08 2022 08:44:38

%S 1,1,1,1,1,9,49,57,-447,5169,78561,-93807,-5655231,31981689,

%T 1014069393,-3857766903,-187639949439,1058896281825,51144433721793,

%U -286891166986335,-16631972691697791,108826313005021545

%N Expansion of e.g.f. exp(arctanh(arctan(x))).

%H G. C. Greubel, <a href="/A012260/b012260.txt">Table of n, a(n) for n = 0..450</a>

%e E.g.f. = 1 + x + x^2/2! + x^3/3! + x^4/4! + 9*x^5/5! + ...

%p seq(coeff(series(factorial(n)*exp(arctanh(arctan(x))),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Oct 29 2018

%t With[{nn=30},CoefficientList[Series[Exp[ArcTanh[ArcTan[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Ray Chandler_, Nov 28 2016 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(atan(x))))) \\ _G. C. Greubel_, Oct 28 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Arctan(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // _G. C. Greubel_, Oct 28 2018

%K sign

%O 0,6

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