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

Author

Clark Kimberling

Keywords

• nonn

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

Crossrefs

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

Programs

Magma

R:=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

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 *)

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

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

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