%I #19 Mar 10 2022 17:34:24
%S 1,1,2,9,48,305,2400,22057,230272,2708001,35412480,509177801,
%T 7986468864,135718942801,2483729876992,48699677975145,
%U 1018542257111040,22634000289407297,532557637644976128,13226748101381102473,345792863300174479360,9492229607399841038961
%N E.g.f.: 1/(1 - x*cosh(x)).
%C Radius of convergence of e.g.f. is |x| < r where r = 0.7650099545507... satisfies cosh(r) = 1/r. See A069814.
%H Vincenzo Librandi, <a href="/A205571/b205571.txt">Table of n, a(n) for n = 0..200</a>
%F a(2*n-1) == 1 (mod 4), a(2*n+2) == 0 (mod 4), for n>=1.
%F a(n) ~ n!/(1+r*sqrt(1-r^2))*(1/r)^n, where r = 0.7650099545507321... is the root of the equation r*cosh(r)=1. - _Vaclav Kotesovec_, Feb 13 2013
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * (2*k+1) * a(n-2*k-1). - _Ilya Gutkovskiy_, Mar 10 2022
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 305*x^5/5! +...
%t CoefficientList[Series[1/(1-x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Feb 13 2013 *)
%o (PARI) {a(n)=n!*polcoeff(1/(1-x*cosh(x +x*O(x^n))),n)}
%Y Cf. A069814, A352252.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 28 2012