A026673 a(n) = T(2n,n-2), T given by A026670.

1, 7, 37, 177, 808, 3596, 15764, 68446, 295294, 1268356, 5430734, 23199304, 98933705, 421352919, 1792709561, 7621345733, 32380443643, 137504761035, 583684770103, 2476836131227, 10507517431481, 44566369523517, 188988331406117

Offset

2,2

Comments

Also a(n) = T(2n,n-2) = T(2n+1,n+2), T given by A026725.

Also a(n) = T(2n,n-2), T given by A026736.

Column k=6 of triangle A236830. - Philippe Deléham, Feb 02 2014

Links

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

Formula

G.f.: (x^2*C(x)^6)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - Philippe Deléham, Feb 02 2014

-(n+2)*(3*n-7)*a(n) +2*(12*n^2-19*n-16)*a(n-1) +5*(-9*n^2+27*n-22)*a(n-2) -2*(3*n-4)*(2*n-3)*a(n-3)=0. - R. J. Mathar, Oct 26 2019

Mathematica

Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^6/(8*x^2*(8*x^2-(1-Sqrt[1 - 4*x])^3)), {x, 0, 30}], x], 2] (* G. C. Greubel, Jul 16 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec( (1-sqrt(1-4*x))^6/(8*x^2*(8*x^2 -(1-sqrt(1-4*x))^3))) \\ G. C. Greubel, Jul 16 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(  (1-Sqrt(1-4*x))^6/(8*x^2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // G. C. Greubel, Jul 16 2019
(Sage) a=((1-sqrt(1-4*x))^6/(8*x^2*(8*x^2 -(1-sqrt(1-4*x))^3))).series(x, 30).coefficients(x, sparse=False); a[2:] # G. C. Greubel, Jul 16 2019

Crossrefs

Cf. A000108, A026670, A026725, A026736, A236830.

Sequence in context: A125317 A006419 A277178 * A026878 A026862 A026889

Adjacent sequences: A026670 A026671 A026672 * A026674 A026675 A026676

Keyword

nonn

Author

Clark Kimberling

Status

approved