OFFSET
0,3
COMMENTS
Radius of convergence of e.g.f. is |x| < r where r = 0.703290658863965... satisfies cos(r) = sinh(r).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(2^n + k) == a(k) (mod 2^n) for k>=0, n>=1 (conjecture).
E.g.f.: E(x) = 1/(cos(x) - sinh(x)) = 1/G(0) where G(k)= 1 -x/(4*k +1 - x*(4*k +1)/(4*k + 2 + x - 2*x*(2*k+1)/(4*k + 3 + x- x*(4*k+3)/(x -4*(k+1)/G(k+1))))); Radius of convergence of e.g.f.E(x)=1/G(0) is infinity; (continued fraction, 3rd kind, 5-step). - Sergei N. Gladkovskii, Jun 08 2012, Oct 03 2012
a(n) ~ n! * 2*exp(r)/((2*sin(r)*exp(r)+exp(2*r)+1)*r^(n+1)), where r = 0.7032906588639654... is defined in the comment. - Vaclav Kotesovec, Sep 22 2013
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 73*x^4/4! + 521*x^5/5! +...
MATHEMATICA
CoefficientList[Series[1/(Cos[x]-Sinh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 22 2013 *)
PROG
(PARI) {a(n)=n!*polcoeff(1/(cos(x+x*O(x^n)) - sinh(x+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 29 2012
STATUS
approved