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%I #10 Feb 07 2015 03:59:39
%S 1,6,140,7616,731856,108552224,22943169600,6543956234752,
%T 2420812240335104,1126850609820597760,644442125440553221120,
%U 444134934522130204704768,363006744066808568769433600
%N tan(sec(x)*arcsin(x))=x+6/3!*x^3+140/5!*x^5+7616/7!*x^7+731856/9!*x^9...
%H Vaclav Kotesovec, <a href="/A012785/b012785.txt">Table of n, a(n) for n = 0..200</a>
%H Vaclav Kotesovec, <a href="/A012785/a012785.jpg">Graph - abs(e.g.f.) in the complex plane</a>
%F a(n) ~ 4 * cos(r) * (2*n+1)! / ((2/sqrt(1-r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.85667809568102855617374657046258339292906641041135819687798... is the root of the equation sec(r)*arcsin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015
%t With[{nn=30},Take[CoefficientList[Series[Tan[Sec[x]ArcSin[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Nov 26 2014 *)
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)