A026852 a(n) = T(2n,n+3), T given by A026736.

1, 8, 45, 221, 1016, 4506, 19572, 83950, 357310, 1513513, 6392134, 26948764, 113500985, 477801129, 2011058681, 8464967333, 35637556603, 150075181365, 632191803847, 2664023530675, 11229995113561, 47355649431833, 199760722776165

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A000108, A026736.

Programs

Magma

R:=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

Mathematica

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 *)

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

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

Formula

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

a(n) ~ (2 + sqrt(5))^(n+3) * (3 - sqrt(5))^7 / (128*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019