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%I #21 Feb 05 2015 11:29:35
%S 0,1,2,7,36,285,2470,25891,304584,4116473,61307338,1011045759,
%T 18130445036,353222430613,7401849057902,166375042595867,
%U 3987022624401808,101564702642995953,2738893925584229778,77978462505905882103,2336771614133464558516,73533230212519134743821
%N E.g.f.: tan(arctanh(x)*exp(x)).
%F a(n) ~ n! * (sin(exp(r) * arctanh(r)))^2 / (exp(r) * (arctanh(r) + 1/(1-r^2)) * r^(n+1)), where r = 0.6673395955783244309800035195157735575759307410912847... is the root of the equation arctanh(r)*exp(r) = Pi/2. - _Vaclav Kotesovec_, Feb 05 2015
%e tan(arctanh(x)*exp(x)) = x+2/2!*x^2+7/3!*x^3+36/4!*x^4+285/5!*x^5...
%t With[{nn=20},CoefficientList[Series[Tan[ArcTanh[x]Exp[x]],{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Mar 05 2013 *)
%o (PARI) x='x+O('x^66); concat([0],Vec(serlaplace(tan(atanh(x)*exp(x))))) \\ _Joerg Arndt_, Mar 05 2013
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E a(0) = 0 added by _Harvey P. Dale_, Mar 05 2013
%E Offset corrected by _Vaclav Kotesovec_, Feb 05 2015