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

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

%S 1,0,0,0,-12,60,-570,3780,-33600,266112,-2452200,21323280,-195333336,

%T 1587135264,-9944442144,-30963922080,3059476293120,-90038301262976,

%U 2195425718875200,-50367095018001792,1140534839454383488

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

%H G. C. Greubel, <a href="/A009077/b009077.txt">Table of n, a(n) for n = 0..250</a>

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

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

%K sign,easy

%O 0,5

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997