A026856 a(n) = T(2n+1,n+3), T given by A026736.

1, 7, 36, 166, 729, 3125, 13229, 55637, 233227, 976271, 4085016, 17096524, 71590557, 299993227, 1258076725, 5280194087, 22178492943, 93226087229, 392144055809, 1650570659359, 6951524807631, 29292822272697, 123496979334851

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000108, A026736.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-Sqrt(1-4*x))^6/(64*x^6*(1-x/Sqrt(1-4*x))) )); // G. C. Greubel, Jul 21 2019

Mathematica

CoefficientList[Series[(1-Sqrt[1-4x])^6/(64*x^6*(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)

PARI

my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^6/(64*x^6*(1-x/sqrt(1-4*x))) ) \\ G. C. Greubel, Jul 21 2019

Sage

((1-sqrt(1-4*x))^6/(64*x^6*(1-x/sqrt(1-4*x)))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 21 2019

Formula

G.f.: (x^2 * C(x)^6)/(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))^6 * (2 + sqrt(5))^(n+3) / (64*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019