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

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A000108, A026736.

Programs

Magma

R:=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

Mathematica

CoefficientList[ Series[(1-Sqrt[1-4x])^3/(8x^3(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)

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

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

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