A009084 - OEIS

%I #19 Sep 08 2022 08:44:37

%S 1,0,-1,3,-2,-40,314,-1134,-3044,87408,-733636,1835020,43592176,

%T -792796368,6272579312,14019198480,-1257528653744,20065121039744,

%U -124527163941136,-2075494412476368,75585686698926496,-1110720454454795520

%N Expansion of e.g.f.: cos(tanh(log(1+x))).

%H G. C. Greubel, <a href="/A009084/b009084.txt">Table of n, a(n) for n = 0..250</a>

%e cos(tanh(log(1+x))) = 1 +0*x/1! -1*x^2/2! +3*x^3/3! -2*x^4/4! -40*x^5/5! +...

%t With[{nn=30},CoefficientList[Series[Cos[Tanh[Log[1+x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 07 2012 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(tanh(log(1+x))))) \\ _G. C. Greubel_, Jul 24 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Tanh(Log(1+x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 24 2018

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Definition clarified by _Harvey P. Dale_, Sep 07 2012