%I #11 Nov 20 2016 03:22:12
%S 1,1,-1,0,9,-20,65,406,-511,21624,88577,1053426,14764321,143838916,
%T 2193647521,29669704702,457719400449,7433158061552,128311987616769,
%U 2329120580336746,45112841958764321,905762343424701116
%N Expansion of e.g.f. exp(arctanh(x)/exp(x)).
%H G. C. Greubel, <a href="/A013573/b013573.txt">Table of n, a(n) for n = 0..400</a>
%e exp(arctanh(x)/exp(x)) = 1 + x - 1/2!*x^2 + 9/4!*x^4 - 20/5!*x^5 + 65/6!*x^6 ...
%t With[{nn = 50}, CoefficientList[Series[Exp[ArcTanh[x]/Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* _G. C. Greubel_, Nov 20 2016 *)
%o (PARI) x='x + O('x^50); Vec(serlaplace(exp(atanh(x)/exp(x)))) \\ _G. C. Greubel_, Nov 20 2016
%K sign
%O 0,5
%A Patrick Demichel (patrick.demichel(AT)hp.com)