A098272 a(n) = 2^(2n+1) * binomial(3n,n)/(2n+1).

2, 8, 96, 1536, 28160, 559104, 11698176, 254017536, 5670567936, 129328742400, 3000426823680, 70587116421120, 1679973370822656, 40376795886780416, 978590323955466240, 23890230876435382272, 586939535850605641728

Offset: 0

Author

Ralf Stephan, Sep 02 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• M. Bousquet-Mélou, Walks in the quarter plane: Kreweras' algebraic model, arXiv:math/0401067 [math.CO], 2004-2006.

Crossrefs

Cf. A001764, A006335.

Programs

Magma

[2^(2*n+1)*Binomial(3*n, n)/(2*n+1): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011

Mathematica

Table[2^(2n+1) Binomial[3n,n]/(2n+1),{n,0,20}] (* Harvey P. Dale, Oct 02 2011 *)

PARI

a(n)=2^(2*n+1)*binomial(3*n,n)/(2*n+1)

PARI

a(n)=polcoeff(serreverse(Ser(x/(2+x^3))),3*n+1)

Formula

G.f. satisfies A(x) = Sum_{n>=0} a(n)*x^(3n+1) = x(2 + A(x)^3).

a(n) = 2n * A006335(n) = 2^(2n+1) * A001764(n).

G.f.: (2 sin(1/3*arcsin(3*sqrt(3)*sqrt(x))))/(sqrt(3)*sqrt(x)). - Harvey P. Dale, Oct 02 2011

E.g.f.: 2*2F2(1/3,2/3; 1,3/2; 27*x). - Ilya Gutkovskiy, Jan 25 2017