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A119309 a(n) = binomial(2*n,n) * 6^n. 3
1, 12, 216, 4320, 90720, 1959552, 43110144, 960740352, 21616657920, 489977579520, 11171488813056, 255928652808192, 5886359014588416, 135839054182809600, 3143703825373593600, 72933928748667371520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of lattice paths from (0,0) to (n,n) using three kinds of steps (1,0) and two kinds of steps (0,1). - Joerg Arndt, Jul 01 2011

Central terms of the triangles in A013620 and A038220.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..400

FORMULA

a(n) = A000984(n) * A000400(n).

G.f.: 1/sqrt(1-24*x). - Zerinvary Lajos, Dec 20 2008 [Corrected by Joerg Arndt, Jul 01 2011]

EXAMPLE

a(3) = binomial(2*3,3) * (6^3) = 20 * 216 = 4320. - Indranil Ghosh, Mar 03 2017

MATHEMATICA

Table[Binomial[2n, n]*(6^n), {n, 0, 15}] (* Indranil Ghosh, Mar 03 2017 *)

PROG

(PARI) /* same as in A092566 but use */

steps=[[1, 0], [1, 0], [1, 0], [0, 1], [0, 1]]; /* note repeated entries */

/* Joerg Arndt, Jun 30 2011 */

(PARI) a(n)=binomial(2*n, n)*6^n \\ Charles R Greathouse IV, Mar 03 2017

(Python)

import math

f=math.factorial

def C(n, r): return f(n)/f(r)/f(n-r)

def A119309(n): return C(2*n, n)*(6**n) # Indranil Ghosh, Mar 03 2017

CROSSREFS

Sequence in context: A116164 A268369 A091266 * A034788 A082165 A006689

Adjacent sequences:  A119306 A119307 A119308 * A119310 A119311 A119312

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 14 2006

STATUS

approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)