A054122 T(2n,n), array T as in A054120.

1, 3, 18, 114, 750, 5058, 34692, 240852, 1687446, 11906610, 84490428, 602335836, 4310670156, 30950436468, 222844189320, 1608369633384, 11632913018598, 84294762019218, 611831430746124, 4447397950230540

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A069835.

Programs

Mathematica

Table[SeriesCoefficient[(1-x)/Sqrt[1-8*x+4*x^2],{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 09 2012 *)

PARI

a(n)=(2*pollegendre(n,2) - pollegendre(n-1,2))<<(n-1) \\ Charles R Greathouse IV, Mar 18 2017

Formula

a(n) = A069835(n) - A069835(n-1).

G.f.: (1-x)/sqrt(1-8*x+4*x^2). - Vladeta Jovovic, May 13 2003

D-finite with recurrence: (n-1)*n*a(n) = 4*(n-1)*(2*n-1)*a(n-1) - 4*(n-2)*n*a(n-2). - Vaclav Kotesovec, Oct 09 2012

a(n) ~ sqrt(6+4*sqrt(3))*(4+2*sqrt(3))^n/(4*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 09 2012

D-finite with recurrence n*a(n) +3*(-3*n+2)*a(n-1) +12*(n-2)*a(n-2) +4*(-n+3)*a(n-3)=0. - R. J. Mathar, Jun 13 2013