OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: C(x)^2/(1 - x/sqrt(1-4*x)) where C(x) = g.f. for Catalan numbers A000108. - David Callan, Jan 16 2016
a(n) ~ (3 - sqrt(5))^2 * (2 + sqrt(5))^(n+1) / (4*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-4x])^2/(4x^2(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)
PROG
(PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^2/(4*x^2*(1-x/sqrt(1-4*x))) ) \\ G. C. Greubel, Jul 21 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^2/(4*x^2*(1-x/Sqrt(1-4*x))) )); // G. C. Greubel, Jul 21 2019
(Sage) ((1-sqrt(1-4*x))^2/(4*x^2*(1-x/sqrt(1-4*x)))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 21 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved