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

3,2

Links

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

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

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A000108, A026736.

Sequence in context: A002696 A016208 A216540 * A317405 A110609 A201190

Adjacent sequences: A026849 A026850 A026851 * A026853 A026854 A026855

Keyword

nonn

Author

Clark Kimberling

Status

approved