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%I #12 Jul 18 2013 15:38:35
%S 1,1,3,14,81,596,5283,54424,641281,8502736,125240163,2029253984,
%T 35869368081,686861235776,14164446354243,312963554690944,
%U 7375924232388481,184700508637993216,4897149234545267523,137056511022745378304,4037684687434825670481
%N E.g.f.: 1/(cos(x) - sin(x)*cosh(x)).
%C Radius of convergence of e.g.f. is |x| < r, where r = 0.678886646361824692... satisfies tan(r) = 1/cosh(r).
%H Vincenzo Librandi, <a href="/A205580/b205580.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ n!/((sin(r)+cos(r)*cosh(r)+sin(r)*sinh(r))*r^(n+1)), where r = 0.678886646... is the root of the equation sin(r)*cosh(r)=cos(r). - _Vaclav Kotesovec_, Jun 27 2013
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 14*x^3/3! + 81*x^4/4! + 596*x^5/5! +...
%t CoefficientList[Series[1/(Cos[x]-Sin[x]*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%o (PARI) {a(n)=n!*polcoeff(1/(cos(x+x*O(x^n)) -sin(x+x*O(x^n)) *cosh(x+x*O(x^n))), n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 29 2012
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