OFFSET
0,2
COMMENTS
Hankel transform is the (4,5) Somos-4 sequence A174404.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1540
FORMULA
G.f.: (1/(2*x))*(1-sqrt((1-2*x^2)/(1+4*x-2*x^2))) = (sqrt(2*x^2-4*x-1)-sqrt(2*x^2-1))/(2*x*sqrt(2*x^2-4*x-1));
G.f.: 1/(1+4x-2x^2-x/(1-x/(1+4x-2x^2-x/(1-x/(1+4x-2x^2-x/(1-x/(1-... (continued fraction).
Conjecture: (n+1)*a(n) +2*(2n+1)*a(n-1) +4*(1-n)*a(n-2) +4*(5-2n)*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 17 2011
a(n) ~ (-1)^n * (2 + sqrt(6))^(n+1) / (2^(3/4) * 3^(1/4) * sqrt(Pi*n)). - Vaclav Kotesovec, Aug 15 2018
MATHEMATICA
CoefficientList[Series[(1/(2*x))*(1 - Sqrt[(1-2*x^2)/(1+4*x-2*x^2)]), {x, 0, 50}], x] (* G. C. Greubel, Aug 14 2018 *)
PROG
(PARI) x='x+O('x^50); Vec((1/(2*x))*(1-sqrt((1-2*x^2)/(1+4*x-2*x^2)))) \\ G. C. Greubel, Aug 14 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1/(2*x))*(1-Sqrt((1-2*x^2)/(1+4*x-2*x^2))))); // G. C. Greubel, Aug 14 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Jan 09 2011
STATUS
approved