%I #36 Aug 19 2022 13:46:54
%S 0,1,2,1,-4,1,62,1,-1384,1,50522,1,-2702764,1,199360982,1,
%T -19391512144,1,2404879675442,1,-370371188237524,1,69348874393137902,
%U 1,-15514534163557086904,1,4087072509293123892362,1,-1252259641403629865468284,1
%N Expansion of e.g.f. tanh(x)*exp(x).
%F E.g.f. tanh(x)*exp(x).
%F G.f.: x/U(0)/(1-x) where U(k) = 1 - x + x^2*(k+1)*(k+2)/U(k+1); (continued fraction, 1-step). - _Sergei N. Gladkovskii_, Oct 14 2012
%F G.f.: x/(1-x)/Q(0), where Q(k) = 1 + x - x*(k+2)/(1+x*(k+1)/Q(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Apr 21 2013
%F If n is even, a(n) ~ (-1)^(1+n/2) * n! * 2^(n+2)/Pi^(n+1). - _Vaclav Kotesovec_, Oct 23 2013
%p G(x):=exp(x)*tanh(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..27 ); # _Zerinvary Lajos_, Apr 05 2009
%t With[{nn=30},CoefficientList[Series[Tanh[x]Exp[x],{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Aug 18 2012 *)
%o (PARI) x='x+O('x^66); concat([0], Vec(serlaplace( tanh(x)*exp(x) ) ) ) \\ _Joerg Arndt_, Apr 21 2013
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition clarified by _Harvey P. Dale_, Aug 18 2012