A205580 E.g.f.: 1/(cos(x) - sin(x)*cosh(x)).

1, 1, 3, 14, 81, 596, 5283, 54424, 641281, 8502736, 125240163, 2029253984, 35869368081, 686861235776, 14164446354243, 312963554690944, 7375924232388481, 184700508637993216, 4897149234545267523, 137056511022745378304, 4037684687434825670481

Offset

0,3

Comments

Radius of convergence of e.g.f. is |x| < r, where r = 0.678886646361824692... satisfies tan(r) = 1/cosh(r).

Links

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

Formula

a(n) ~ n!/((sin(r)+cos(r)*cosh(r)+sin(r)*sinh(r))*r^(n+1)), where r = 0.678886646... is the root of the equation sin(r)*cosh(r)=cos(r). - Vaclav Kotesovec, Jun 27 2013

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 14*x^3/3! + 81*x^4/4! + 596*x^5/5! +...

Mathematica

CoefficientList[Series[1/(Cos[x]-Sin[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)) -sin(x+x*O(x^n)) *cosh(x+x*O(x^n))), n)}

Crossrefs

Sequence in context: A077054 A355291 A325219 * A352151 A032332 A032080

Adjacent sequences: A205577 A205578 A205579 * A205581 A205582 A205583

Keyword

nonn

Author

Paul D. Hanna, Jan 29 2012

Status

approved