A205572 E.g.f.: 1/(cos(x) - sinh(x)).

1, 1, 3, 13, 73, 521, 4443, 44213, 502993, 6436561, 91520883, 1431459613, 24424457113, 451474855001, 8987248462923, 191682800678213, 4360821252342433, 105410131831623841, 2697863748098734563, 72885101748061044013, 2072687894252786558953

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

Sequence in context: A059294 A124468 A352302 * A128196 A367747 A162161

Adjacent sequences: A205569 A205570 A205571 * A205573 A205574 A205575

Keyword

nonn

Author

Paul D. Hanna, Jan 29 2012

Status

approved