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Expansion of e.g.f.: cos(log(1+x)^2).
1

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

%S 1,0,0,0,-12,120,-1020,8820,-79548,746928,-7222560,70422000,

%T -663291552,5383325376,-19385922192,-677619961200,27837247597392,

%U -777514428757632,19561790897109504,-475628128967428992,11488209552378045888

%N Expansion of e.g.f.: cos(log(1+x)^2).

%H G. C. Greubel, <a href="/A009035/b009035.txt">Table of n, a(n) for n = 0..250</a>

%t With[{nn=20},CoefficientList[Series[Cos[Log[1+x]^2],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 30 2015 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cos(log(1+x)^2))) \\ _G. C. Greubel_, Jul 22 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Log(1+x)^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 22 2018

%K sign,easy

%O 0,5

%A _R. H. Hardin_

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

%E Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Jan 30 2015