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%I #19 Jan 02 2014 17:53:49
%S 0,1,6,135,6300,503685,61434450,10620124515,2471073204600,
%T 744907219281225,282494651079390750,131664032748125452575,
%U 73997676994079578439700,49364071776588936300058125,38571353476865946088188086250,34900798662291878654547561226875
%N E.g.f.: -arcsin(log(x+1)-arctanh(x)) (even powers only).
%F a(n) = (2n)! * [x^(2n)] -arcsin(log(x+1)-arctanh(x)).
%F a(n) ~ 2^(2*n) * n^(2*n-1) / (1/(exp(1)-sqrt(exp(2)-1)) - exp(1))^(2*n-1). - _Vaclav Kotesovec_, Jan 02 2014
%e +arcsin(log(x+1)-arctanh(x)) = 0 -1/2!*x^2 -6/4!*x^4 -135/6!*x^6 -6300/8!*x^8...
%t With[{nn=40},Take[CoefficientList[Series[-ArcSin[Log[x+1]-ArcTanh[x]],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jul 22 2013 *)
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Zero prepended by and more terms from _Harvey P. Dale_, Jul 22 2013
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