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Expansion of e.g.f. cos(tan(log(1+x))).
1

%I #14 Sep 08 2022 08:44:37

%S 1,0,-1,3,-18,120,-966,8946,-93748,1094832,-14078036,197375420,

%T -2992213584,48700300272,-845573085072,15571699693200,

%U -302493769715504,6165508375224704,-131129003401938832,2892534929270217648

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

%H G. C. Greubel, <a href="/A009065/b009065.txt">Table of n, a(n) for n = 0..250</a>

%t With[{nmax = 30}, CoefficientList[Series[Cos[Tan[Log[1 + x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 24 2018 *)

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

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Tan(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 GĂ©rard_, Mar 15 1997