A026853 a(n) = T(2n,n+4), T given by A026736.

1, 10, 66, 365, 1837, 8741, 40133, 179932, 793605, 3460106, 14961664, 64306917, 275180827, 1173714565, 4994096327, 21211537533, 89972566673, 381261067469, 1614446775255, 6832832045575, 28908094009481, 122272843951891, 517095189163181

Offset

4,2

Links

G. C. Greubel, Table of n, a(n) for n = 4..1000

Formula

G.f.: x^4*C(x)^9/(1 -x/sqrt(1-4*x)), where C(x) if the g.f. for Catalan numbers A000108. - G. C. Greubel, Jul 17 2019

a(n) ~ (3 - sqrt(5))^9 * (2 + sqrt(5))^(n+4) / (512*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019

Mathematica

Drop[CoefficientList[Series[Sqrt[1-4x]*(1-Sqrt[1-4x])^9/(512*x^5*(Sqrt[1-4x]-x)), {x, 0, 40}], x], 4] (* G. C. Greubel, Jul 17 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x) -x)) ) \\ G. C. Greubel, Jul 17 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^9/(512*x^5*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x)-x))).series(x, 40).coefficients(x, sparse=False); a[4:] # G. C. Greubel, Jul 17 2019

Crossrefs

Cf. A000108, A026736.

Sequence in context: A080421 A320817 A004310 * A177452 A033504 A163615

Adjacent sequences: A026850 A026851 A026852 * A026854 A026855 A026856

Keyword

nonn

Author

Clark Kimberling

Status

approved