A205569 - OEIS

%I #13 Jul 18 2013 11:29:44

%S 1,2,6,30,216,1930,20400,251174,3541888,56226258,991514880,

%T 19230159982,406873353216,9326318738906,230222431688704,

%U 6089006394645750,171780282479247360,5149076226504182434,163421449125050253312,5474820500060681776574

%N E.g.f.: 1/(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="/A205569/b205569.txt">Table of n, a(n) for n = 0..200</a>

%F a(2*n-1) == 2 (mod 4), a(2*n+2) == 0 (mod 4), for n>=1.

%F a(n) ~ n! * exp(c*n)/((1-c)*(1+c)^2), where c = LambertW(1) = 0.5671432904... - _Vaclav Kotesovec_, Jun 26 2013

%e E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 30*x^3/3! + 216*x^4/4! + 1930*x^5/5! +...

%t CoefficientList[Series[1/(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/(1+x^2-2*x*cosh(x +x*O(x^n))),n)}

%Y Cf. A205570.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 28 2012