%I #17 Sep 08 2022 08:44:49

%S 1,7,37,177,808,3596,15764,68446,295294,1268356,5430734,23199304,

%T 98933705,421352919,1792709561,7621345733,32380443643,137504761035,

%U 583684770103,2476836131227,10507517431481,44566369523517,188988331406117

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

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

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

%C Column k=6 of triangle A236830. - _Philippe Deléham_, Feb 02 2014

%H G. C. Greubel, <a href="/A026673/b026673.txt">Table of n, a(n) for n = 2..1000</a>

%F 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

%F -(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

%t 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 *)

%o (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

%o (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

%o (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

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

%K nonn

%O 2,2

%A _Clark Kimberling_