A026854 a(n) = T(2n+1,n+1), T given by A026736.

1, 3, 10, 36, 136, 530, 2109, 8515, 34739, 142817, 590537, 2452639, 10221505, 42714623, 178888442, 750500716, 3153137436, 13263180550, 55844218906, 235323138044, 992316962382, 4186870456952, 17674378119680, 74641954142026

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

Cf. A000108, A026736.

Sequence in context: A122448 A007582 A369436 * A136576 A129156 A317775

Adjacent sequences: A026851 A026852 A026853 * A026855 A026856 A026857

Keyword

nonn

Author

Clark Kimberling

Status

approved