A024485 a(n) = (2/(3*n-1))*binomial(3*n,n).

-2, 3, 6, 21, 90, 429, 2184, 11628, 63954, 360525, 2072070, 12096045, 71524440, 427496076, 2578547760, 15675792072, 95951017602, 590842763469, 3657598059570, 22749427475775, 142096423925610, 890949529108485, 5605635937900320, 35380499289211440, 223951032734902200

Offset

0,1

Comments

For n >= 1, a(n) is the number of lattice paths from (0,0) to (2n,n) using only the steps (1,0) and (0,1) and which do not touch the line y = x/2 except at the path's endpoints. - Lucas A. Brown, Aug 21 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Formula

G.f.: 3*g-2 where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011

a(n) = 2*A005809(n)/(3*n-1). - R. J. Mathar, Apr 27 2020

D-finite with recurrence: 2*n*(2*n-1)*a(n) -3*(3*n-2)*(3*n-4)*a(n-1)=0. - R. J. Mathar, Apr 27 2020

a(n) = A006013(n-1)/3 for n >= 1. - Lucas A. Brown, Aug 21 2020

Maple

[seq((2/(3*n-1))*binomial(3*n, n), n=0..40)];

Mathematica

Table[2/(3n-1) Binomial[3n, n], {n, 0, 20}] (* Harvey P. Dale, Nov 21 2015 *)

Prog

(PARI) a(n) = (2/(3*n-1))*binomial(3*n, n); \\ Michel Marcus, May 10 2020

Crossrefs

Sequence in context: A025239 A127294 A012924 * A013155 A303224 A007501

Adjacent sequences: A024482 A024483 A024484 * A024486 A024487 A024488

Keyword

sign

Author

Clark Kimberling

Extensions

Terms a(21) and beyond from Andrew Howroyd, May 10 2020

Status

approved