OFFSET
0,2
COMMENTS
Radius of convergence of e.g.f. is |x| < r where r = LambertW(1) = exp(-LambertW(1)) = 0.56714329040978...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(2*n-1) == 2 (mod 4), a(2*n+2) == 0 (mod 4), for n>=1.
a(n) ~ n! * exp(c*n)/((1-c)*(1+c)^2), where c = LambertW(1) = 0.5671432904... - Vaclav Kotesovec, Jun 26 2013
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 30*x^3/3! + 216*x^4/4! + 1930*x^5/5! +...
MATHEMATICA
CoefficientList[Series[1/(1+x^2 - 2*x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)
PROG
(PARI) {a(n)=n!*polcoeff(1/(1+x^2-2*x*cosh(x +x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 28 2012
STATUS
approved