OFFSET
0,2
COMMENTS
Hankel transform is 4^n. In general, for r>=0, the sequence given by sum{k=0..n, C(n,floor(k/2))*(-r)^(n-k)} has Hankel transform (r+1)^n. The sequence is the image of the sequence with g.f. (1+x)/(1+3x) under the Chebyshev mapping g(x)->(1/sqrt(1-4x^2))g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: (1/sqrt(1-4x^2))(1+x*c(x^2))/(1+3*x*c(x^2)).
Conjecture: 3*n*a(n) +2*(5*n-3)*a(n-1) +4*(-3*n+1)*a(n-2) +40*(-n+2)*a(n-3)=0. - R. J. Mathar, Nov 15 2012
a(n) ~ (-1)^n * 2^(n+1) * 5^n / 3^(n+1). - Vaclav Kotesovec, Feb 08 2014
G.f.: 1/(-1+2*x+2*sqrt(1-4*x^2)). - Vaclav Kotesovec, Feb 08 2014
MATHEMATICA
CoefficientList[Series[1/(-1+2*x+2*Sqrt[1-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jan 11 2007
EXTENSIONS
More terms from Vincenzo Librandi, Feb 11 2014
STATUS
approved