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%I #11 Jul 18 2013 10:51:03
%S 1,1,2,9,60,485,4680,53557,709968,10662633,178786080,3312164801,
%T 67201649856,1481949570829,35291569832064,902631317654445,
%U 24676916031310080,718135040275928657,22164641043514532352,723163494821506484473,24869366907327781002240
%N E.g.f.: 1/sqrt(1+x^2 - 2*x*cosh(x)).
%C Radius of convergence of e.g.f. is |x| < r where r = LambertW(1) = exp(-LambertW(1)) = 0.56714329040978...
%H Vincenzo Librandi, <a href="/A205570/b205570.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! * exp(c*n)/(sqrt(Pi*n)*(1+c)*sqrt(1-c)), where c = LambertW(1) = 0.5671432904... - _Vaclav Kotesovec_, Jun 26 2013
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 60*x^4/4! + 485*x^5/5! +...
%t CoefficientList[Series[1/Sqrt[1+x^2-2*x*Cosh[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o (PARI) {a(n)=n!*polcoeff(1/sqrt(1+x^2-2*x*cosh(x +x*O(x^n))),n)}
%Y Cf. A205569.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 28 2012