OFFSET
0,4
COMMENTS
A transform of F(n+1) by the inverse of the Riordan array (1, x*(1+x)/(1-2*x)).
Equivalently, row sums of the inverse of the Riordan array (1, x/(2-sqrt(1+4*x)).
Hankel transform is alternating sign version of A083667.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: 1/(1-2*x-2*x^2+x*sqrt(1+8*x+4*x^2)).
Conjecture: (n-1)*a(n) +4*(n-4)*a(n-1) + (65-29*n)*a(n-2) +12*(7-2*n)*a(n-3)+ 4*(4-n)*a(n-4) =0. - R. J. Mathar, Nov 14 2011
a(n) ~ (-1)^n * (5*sqrt(3)-14) * sqrt(2*sqrt(3)-3) * 2^(n+1/2) * (2+sqrt(3))^n / (121 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014
MATHEMATICA
CoefficientList[Series[1/(1-2*x-2*x^2+x*Sqrt[1+8*x+4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)
PROG
(PARI) x='x+O('x^50); Vec(1/(1-2*x-2*x^2+x*sqrt(1+8*x+4*x^2))) \\ G. C. Greubel, Mar 21 2017
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jun 26 2008
STATUS
approved