A026850 a(n) = T(2n,n+1), T given by A026736.

1, 4, 15, 57, 221, 872, 3489, 14113, 57575, 236457, 976271, 4047871, 16840879, 70259892, 293790127, 1230783085, 5164196117, 21696512073, 91254256589, 384165925259, 1618551762085, 6823801074549, 28785680471185, 121490461772347

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

G.f.: (x * C(x)^3)/(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))^3 * (2 + sqrt(5))^(n+1) / (8*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019

Mathematica

CoefficientList[ Series[(1-Sqrt[1-4x])^3/(8x^3(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))^3/(8*x^2*(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))^3/(8*x^2*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^3/(8*x^2*(sqrt(1-4*x) -x))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jul 17 2019

Crossrefs

Cf. A000108, A026736.

Sequence in context: A277924 A371777 A095930 * A109642 A307570 A164589

Adjacent sequences: A026847 A026848 A026849 * A026851 A026852 A026853

Keyword

nonn

Author

Clark Kimberling

Status

approved