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%I
%S 1,1,17,721,58337,7734241,1526099057,419784870961,153563504618177,
%T 72104198836466881,42270463533824671697,30262124466958766778001,
%U 25981973075048213029395617,26350476755161831091778460321
%N Even coefficients in expansion of cos(x)/sqrt(cos(2*x)).
%F E.g.f.: Sum_{k>=0} a(k)x^(2k)/(2k)! = cos(x)/sqrt(cos(2*x)) = sec(arcsin(tan(x))).
%F a(n) ~ 2*sqrt(2/Pi) * n^(2*n) * (8/Pi)^(2*n) / exp(2*n). - _Vaclav Kotesovec_, Oct 07 2013
%e sec(arcsin(tan(x))) = 1+1/2!*x^2+17/4!*x^4+721/6!*x^6+58337/8!*x^8...
%t Table[n!*SeriesCoefficient[Cos[x]/Sqrt[Cos[2*x]],{x,0,n}],{n,0,30,2}] (* _Vaclav Kotesovec_, Oct 07 2013 *)
%o (PARI) {a(n)=local(A); if(n<0, 0, n*=2; A=x*O(x^n); n!*polcoeff( cos(x+A)/sqrt(cos(2*x+A)), n))} /* _Michael Somos_, Jul 18 2005 */
%K nonn
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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