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A098272 a(n) = 2^(2n+1) * binomial(3n,n)/(2n+1). 2
2, 8, 96, 1536, 28160, 559104, 11698176, 254017536, 5670567936, 129328742400, 3000426823680, 70587116421120, 1679973370822656, 40376795886780416, 978590323955466240, 23890230876435382272, 586939535850605641728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

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

MATHEMATICA

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

PROG

(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)

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

CROSSREFS

Cf. A001764, A006335.

Sequence in context: A319125 A297688 A126429 * A087540 A052713 A136797

Adjacent sequences:  A098269 A098270 A098271 * A098273 A098274 A098275

KEYWORD

nonn

AUTHOR

Ralf Stephan, Sep 02 2004

STATUS

approved

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Last modified August 18 07:30 EDT 2019. Contains 326072 sequences. (Running on oeis4.)