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cos(log(x+1)-arctanh(x))=1-3/4!*x^4-90/6!*x^6-4515/8!*x^8...
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%I #6 Mar 17 2019 16:20:53

%S 1,0,-3,-90,-4515,-359100,-42047775,-6839182350,-1478380278375,

%T -410407616619000,-142401495047686875,-60416785362985301250,

%U -30781865895322663996875,-18550414761518537710312500

%N cos(log(x+1)-arctanh(x))=1-3/4!*x^4-90/6!*x^6-4515/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[Cos[Log[x+1]-ArcTanh[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 17 2019 *)

%K sign

%O 0,3

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