A026851 a(n) = T(2n,n+2), T given by A026736.

1, 6, 28, 121, 508, 2109, 8723, 36065, 149277, 618961, 2571503, 10704390, 44641793, 186492242, 780275596, 3269135406, 13713525610, 57588530626, 242068874444, 1018378855512, 4287501276956, 18062827159136, 76141329903018

Offset

2,2

Links

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

Formula

G.f.: (x * C(x)^5)/(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))^5 * (2 + sqrt(5))^(n+2) / (32*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019

D-finite with recurrence -(n+3)*(55*n-136)*a(n) +2*(331*n^2-427*n-1440)*a(n-1) +3*(-867*n^2+2755*n-252)*a(n-2) +2*(1555*n^2-8227*n+11304)*a(n-3) +12*(37*n-89)*(2*n-5)*a(n-4)=0. - R. J. Mathar, Nov 22 2024

Mathematica

CoefficientList[Series[(1-Sqrt[1-4x])^5/(32 x^5 (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))^5/(32*x^3*(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))^5/(32*x^3*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^5/(32*x^3*(sqrt(1-4*x)-x))).series(x, 30).coefficients(x, sparse=False); a[2:] # G. C. Greubel, Jul 17 2019

Crossrefs

Cf. A000108, A026736.

Sequence in context: A037131 A292485 A225417 * A267689 A300996 A181337

Adjacent sequences: A026848 A026849 A026850 * A026852 A026853 A026854

Keyword

nonn,changed

Author

Clark Kimberling

Status

approved