A204808 E.g.f.: 1/(cos(x)*exp(-x) - sin(x)*exp(x)).

1, 2, 10, 72, 700, 8472, 123160, 2088352, 40472080, 882374432, 21375168160, 569584828032, 16557545575360, 521429481796992, 17683975195826560, 642580338425754112, 24905983319537271040, 1025672924970436977152, 44723694658790008015360, 2058484266430604449646592

Offset

0,2

Links

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

Formula

a(2*n) == 0 (mod 5), a(2*n-1) == 2 (mod 5), for n>=1.

a(n) ~ n! * sqrt(sin(2*r)/2)/(1+sin(2*r))*(1/r)^(n+1), where r = 0.41280383453558... is the root of the equation sin(r)*exp(2*r)=cos(r). - Vaclav Kotesovec, Feb 14 2013

Example

E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 72*x^3/3! + 700*x^4/4! + 8472*x^5/5! +...

Mathematica

CoefficientList[Series[1/(Cos[x]/E^x-Sin[x]*E^x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 14 2013 *)

Prog

(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff(1/(cos(X)*exp(-X) - sin(X)*exp(X)), n)}

Crossrefs

Sequence in context: A292406 A185183 A052555 * A084844 A144011 A238085

Adjacent sequences: A204805 A204806 A204807 * A204809 A204810 A204811

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2012

Status

approved