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%I #8 Oct 31 2013 05:24:20
%S 0,0,2,-3,4,-20,398,-3339,20424,-170064,2806362,-43459515,558557580,
%T -7606771380,138088561830,-2820420542835,55165236001680,
%U -1086992549563200,24100477113093810,-594762006770251155
%N arctanh(arcsinh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...
%F a(n) ~ (n-1)!/2 * (-1)^n / (1-exp(r))^n, where r = -1.4265092278500059... is the root of the equation exp(2/r) + 2*exp(1/r) - 2*exp((r^2+1)/r) = 1. - _Vaclav Kotesovec_, Oct 31 2013
%t CoefficientList[Series[ArcTanh[ArcSinh[x]*Log[x+1]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 31 2013 *)
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0, a(1)=0, _Vaclav Kotesovec_, Oct 31 2013