A205576 E.g.f.: 1/(cos(x) - x*cosh(x)).

1, 1, 3, 15, 89, 685, 6331, 67851, 833265, 11509209, 176580211, 2980609863, 54883547465, 1094804661509, 23519070268331, 541334395140675, 13290451105971425, 346691343404639153, 9575683088728787683, 279175712231827548543, 8567653762387524327225

Offset

0,3

Comments

Radius of convergence of e.g.f. is |x| < r where r = 0.6516970063076... satisfies cosh(r) = cos(r)/r.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) ~ n!/((sin(r)+cosh(r)+sinh(r)*r)*r^(n+1)), where r = 0.6516970063... is the root of the equation r*cosh(r) = cos(r). - Vaclav Kotesovec, Jun 27 2013

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 15*x^3/3! + 89*x^4/4! + 685*x^5/5! +...

Mathematica

CoefficientList[Series[1/(Cos[x]-x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Prog

(PARI) {a(n)=n!*polcoeff(1/(cos(x+x*O(x^n))-x*cosh(x+x*O(x^n))), n)}

Crossrefs

Sequence in context: A074541 A368974 A074550 * A173695 A255688 A370186

Adjacent sequences: A205573 A205574 A205575 * A205577 A205578 A205579

Keyword

nonn

Author

Paul D. Hanna, Jan 29 2012

Status

approved