OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
FORMULA
G.f.: (x * C(x)^5)/(1 - x/sqrt(1 - 4 * x)) where C(x) is the g.f. for Catalan numbers A000108. - David Callan, Jan 16 2016
a(n) ~ (3 - sqrt(5))^5 * (2 + sqrt(5))^(n+2) / (32*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-4x])^5/(32 x^5 (1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^5/(32*x^3*(sqrt(1-4*x) -x)) ) \\ G. C. Greubel, Jul 17 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^5/(32*x^3*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^5/(32*x^3*(sqrt(1-4*x)-x))).series(x, 30).coefficients(x, sparse=False); a[2:] # G. C. Greubel, Jul 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved