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%I #10 Nov 01 2013 15:54:43
%S 1,0,0,-3,0,-15,90,-945,2520,-36855,368550,-5145525,31808700,
%T -541215675,7577019450,-134726216625,1338322986000,-27408165159375,
%U 493346972868750,-10700744687758125,147490229469082500
%N exp(arcsinh(x)-arctanh(x)) = 1-3/3!*x^3-15/5!*x^5+90/6!*x^6-945/7!*x^7...
%H Alois P. Heinz, <a href="/A013494/b013494.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (x+sqrt(1+x^2))*sqrt(1-x^2)/(x+1). - _Vaclav Kotesovec_, Nov 01 2013
%F a(n) ~ 2 * (-1)^n * (sqrt(2)-1) * n^n / exp(n). - _Vaclav Kotesovec_, Nov 01 2013
%t CoefficientList[Series[Exp[ArcSinh[x]-ArcTanh[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Nov 01 2013 *)
%K sign
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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