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a(n) = T(2n-1,n-2), T given by A026670. Also T(2n-1,n-2) = T(2n,n+2), T given by A026725 and T(2n,n-2), T given by A026736.
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%I #15 Sep 08 2022 08:44:49

%S 1,6,29,131,575,2488,10681,45641,194467,827045,3512983,14909339,

%T 63239487,268127302,1136495965,4816202207,20406887583,86457399359,

%U 366263778659,1551535465465,6572224024539,27838835937511,117918419518219

%N a(n) = T(2n-1,n-2), T given by A026670. Also T(2n-1,n-2) = T(2n,n+2), T given by A026725 and T(2n,n-2), T given by A026736.

%C Column k=5 of triangle A236830. - _Philippe Deléham_, Feb 02 2014

%H G. C. Greubel, <a href="/A026675/b026675.txt">Table of n, a(n) for n = 2..1000</a>

%F G.f.: (x^2*C(x)^5)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - _Philippe Deléham_, Feb 02 2014

%t Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^5/(4*x*(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))^5/(4*x*(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))^5/(4*x*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // _G. C. Greubel_, Jul 16 2019

%o (Sage) a=((1-sqrt(1-4*x))^5/(4*x*(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_