A205182 E.g.f.: (cosh(x) + sin(x)) / (cos(x) - sinh(x)).

1, 2, 6, 24, 140, 992, 8456, 84224, 957840, 12257792, 174293856, 2726068224, 46514037440, 859790139392, 17115342333056, 365041325441024, 8304761365213440, 200743379109281792, 5137820023434733056, 138802611894431514624, 3947233200665413667840

Offset

0,2

Comments

Unsigned version of A013068, which has offset 1.

Links

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

Formula

E.g.f.: -log(cos(x) - sinh(x)) = Sum_{n>=1} a(n-1)*x^n/n!.

a(n) ~ n! /r^(n+1), where r = 0.7032906588639654... is the root of the equation cos(r) = sinh(r). - Vaclav Kotesovec, Sep 22 2013

Example

E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 24*x^3/3! + 140*x^4/4! + 992*x^5/5! +...
where A(x) = (cosh(x) + sin(x)) / (cos(x) - sinh(x)).
The e.g.f. at offset 1 begins:
B(x) = x + 2*x^2/2! + 6*x^3/3! + 24*x^4/4! + 140*x^5/5! + 992*x^6/6! +...
satisfies exp(B(x)) = 1/(cos(x) - sinh(x)).

Mathematica

CoefficientList[Series[(Cosh[x]+Sin[x])/(Cos[x]-Sinh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 22 2013 *)
Rest[CoefficientList[Series[-Log[Cos[x]-Sinh[x]], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 22 2013 *)

Prog

(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff((cosh(X)+sin(X))/(cos(X)-sinh(X)), n)}

Crossrefs

Cf. A013068.

Sequence in context: A292907 A216507 A366459 * A013068 A326780 A365976

Adjacent sequences: A205179 A205180 A205181 * A205183 A205184 A205185

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2012

Status

approved