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%I #32 Jun 04 2013 08:06:43
%S 1,2,10,72,700,8472,123160,2088352,40472080,882374432,21375168160,
%T 569584828032,16557545575360,521429481796992,17683975195826560,
%U 642580338425754112,24905983319537271040,1025672924970436977152,44723694658790008015360,2058484266430604449646592
%N E.g.f.: 1/(cos(x)*exp(-x) - sin(x)*exp(x)).
%H Vincenzo Librandi, <a href="/A204808/b204808.txt">Table of n, a(n) for n = 0..200</a>
%F a(2*n) == 0 (mod 5), a(2*n-1) == 2 (mod 5), for n>=1.
%F a(n) ~ n! * sqrt(sin(2*r)/2)/(1+sin(2*r))*(1/r)^(n+1), where r = 0.41280383453558... is the root of the equation sin(r)*exp(2*r)=cos(r). - _Vaclav Kotesovec_, Feb 14 2013
%e E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 72*x^3/3! + 700*x^4/4! + 8472*x^5/5! +...
%t CoefficientList[Series[1/(Cos[x]/E^x-Sin[x]*E^x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Feb 14 2013 *)
%o (PARI) {a(n)=local(X=x+x*O(x^n));n!*polcoeff(1/(cos(X)*exp(-X) - sin(X)*exp(X)),n)}
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 21 2012
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