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

2,2

Links

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

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

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 *)

Prog

(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
(Magma) R<x>:=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
(SageMath) ((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

Crossrefs

Cf. A000108, A026736.

Sequence in context: A003516 A095931 A292486 * A038748 A099455 A102053

Adjacent sequences: A026853 A026854 A026855 * A026857 A026858 A026859

Keyword

nonn

Author

Clark Kimberling

Status

approved