A227051 E.g.f.: 1/(cos(x) - sin(x)*sinh(x)), omitting the zero-valued coefficients of odd powers of x.

1, 3, 53, 2333, 191673, 25307913, 4900979093, 1308599657693, 460755584003313, 206844794964734673, 115313659955341400333, 78158334287649490486853, 63294640267864707577746153, 60357724113527363258814802233, 66943314938342593826952764256773, 85443499990582824984241143043808813

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) == 3 (mod 10) for n>0 (conjecture).

a(n) ~ 2*(2*n)! / ((sin(r)+cos(r)*sinh(r)+sin(r)*cosh(r)) * r^(2*n+1)), where r = 0.825607669071161851569946... is the root of the equation sin(r)*sinh(r) = cos(r). - Vaclav Kotesovec, Jul 13 2014

Example

E.g.f.: A(x) = 1 + 3*x^2/2! + 53*x^4/4! + 2333*x^6/6! + 191673*x^8/8! + 25307913*x^10/10! +...

Mathematica

Table[n!*SeriesCoefficient[1/(Cos[x] - Sin[x]*Sinh[x]), {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Jul 13 2014 *)

Prog

(PARI) {a(n)=local(X=x+x*O(x^(2*n))); (2*n)!*polcoeff(1/(cos(X) - sin(X)*sinh(X)), 2*n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A185071.

Sequence in context: A300420 A300683 A296678 * A300606 A301348 A296680

Adjacent sequences: A227048 A227049 A227050 * A227052 A227053 A227054

Keyword

nonn

Author

Paul D. Hanna, Jun 29 2013

Status

approved