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a(n) = T(2n,n+3), T given by A026736.
2

%I #15 Sep 08 2022 08:44:49

%S 1,8,45,221,1016,4506,19572,83950,357310,1513513,6392134,26948764,

%T 113500985,477801129,2011058681,8464967333,35637556603,150075181365,

%U 632191803847,2664023530675,11229995113561,47355649431833,199760722776165

%N a(n) = T(2n,n+3), T given by A026736.

%H G. C. Greubel, <a href="/A026852/b026852.txt">Table of n, a(n) for n = 3..1000</a>

%F G.f.: x^3*C(x)^7/(1 - x/Sqrt(1-4*x)) = x^3*(1-2*x*C(x))*C(x)^9/(1-x*C(x)^3), where C(x) is the g.f. of A000108. - _G. C. Greubel_, Jul 17 2019

%F a(n) ~ (2 + sqrt(5))^(n+3) * (3 - sqrt(5))^7 / (128*sqrt(5)). - _Vaclav Kotesovec_, Jul 18 2019

%t Drop[CoefficientList[Series[Sqrt[1-4*x]*(1-Sqrt[1-4*x])^9/(64*x^4*(8*x^2 -(1-Sqrt[1-4*x])^3)), {x, 0, 40}], x], 3] (* _G. C. Greubel_, Jul 17 2019 *)

%o (PARI) my(x='x+O('x^40)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(64*x^4*(8*x^2 -(1 - sqrt(1-4*x))^3 ))) \\ _G. C. Greubel_, Jul 17 2019

%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^9/(64*x^4*(8*x^2 -(1-Sqrt(1-4*x))^3 )) )); // _G. C. Greubel_, Jul 17 2019

%o (Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(64*x^4*(8*x^2 -(1-sqrt(1-4*x))^3 ))).series(x, 45).coefficients(x, sparse=False); a[3:40] # _G. C. Greubel_, Jul 17 2019

%Y Cf. A000108, A026736.

%K nonn

%O 3,2

%A _Clark Kimberling_