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A153231 a(n) = 2^n * binomial(3n,n)/(2n+1). 5
1, 2, 12, 96, 880, 8736, 91392, 992256, 11075328, 126297600, 1465052160, 17233182720, 205074874368, 2464404045824, 29864206663680, 364535993597952, 4477993284993024, 55316387638149120, 686720560048373760, 8563155161736806400, 107206525476085432320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of rooted generalized noncrossing trees on n+1 vertices.

The series reversion of y=x+2*x^3 is x= y -2*y^3 +12*y^5 -96*y^7 +880*y^9 -8736*y^11+... - R. J. Mathar, Sep 29 2012

Lattice paths in the 1st quadrant from (0,0) to (3n,0) using steps D(1,-1) and two types of U(1,2). - David Scambler, Jun 22 2013

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..889

Hsien-Kuei Hwang, Mihyun Kang, Guan-Huei Duh, Asymptotic Expansions for Sub-Critical Lagrangean Forms, LIPIcs Proceedings of Analysis of Algorithms 2018, Vol. 110. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2018.

Anssi Yli-Jyrä and Carlos Gómez-Rodríguez, Generic Axiomatization of Families of Noncrossing Graphs in Dependency Parsing, arXiv:1706.03357 [cs.CL], 2017.

FORMULA

a(n) = 2^n*A001764(n). - R. J. Mathar, Oct 06 2012

n*(2*n+1)*a(n) -3*(3*n-1)*(3*n-2)*a(n-1)=0. - R. J. Mathar, Nov 16 2012

a(n) = (n+1)*A000309(n). - Johannes W. Meijer, Aug 22 2013

G.f.: sqrt(2)/sqrt(3*x)*sin(1/3*asin(sqrt(27*x/2))). - Vladimir Kruchinin, Sep 08 2015

E.g.f.: 2F2(1/3,2/3; 1,3/2; 27*x/2). - Ilya Gutkovskiy, Nov 23 2017

MATHEMATICA

Table[2^n Binomial[3 n, n]/(2 n + 1), {n, 0, 25}] (* Vincenzo Librandi, Sep 08 2015 *)

PROG

(MAGMA) [2^n*Binomial(3*n, n)/(2*n+1): n in [0..30]]; // Vincenzo Librandi, Sep 08 2015

(PARI) a(n) = 2^n*binomial(3*n, n)/(2*n+1); \\ Altug Alkan, Sep 24 2018

CROSSREFS

Sequence in context: A322543 A213422 A307103 * A052564 A014297 A193425

Adjacent sequences:  A153228 A153229 A153230 * A153232 A153233 A153234

KEYWORD

nonn

AUTHOR

Yidong Sun (sydmath(AT)yahoo.com.cn), Dec 21 2008

EXTENSIONS

More terms from N. J. A. Sloane, Dec 21 2008

STATUS

approved

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Last modified October 18 00:21 EDT 2019. Contains 328135 sequences. (Running on oeis4.)