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%I #7 Feb 03 2015 11:15:47
%S 0,2,-1,17,-54,685,-4950,66265,-757400,11694805,-178921800,3236694875,
%T -61062375000,1283939654075,-28563558478000,688487451426125,
%U -17578710756204000,478975365932337625,-13780824752845800000
%N tan(arcsinh(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4+685/5!*x^5...
%F a(n) ~ n! * (1+r) * sqrt(1 + r^2) * sin(log((1+r) * (r + sqrt(1 + r^2))))^2 / ((1+r + sqrt(1 + r^2)) * r^(n+1)), where r = (-1 - exp(Pi/2) + exp(-Pi/4) * sqrt(2 + 2*exp(Pi/2))) / (2 + exp(Pi/2)) = -0.62494974755855577154785... . - _Vaclav Kotesovec_, Feb 03 2015
%t CoefficientList[Series[Tan[ArcSinh[x] + Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 03 2015 *)
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Feb 03 2015
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