A079590 a(n) = C(6*n+1,n).

1, 7, 78, 969, 12650, 169911, 2324784, 32224114, 450978066, 6358402050, 90177170226, 1285063345176, 18385569737808, 263926640438545, 3799541229226200, 54834293825867556, 793067310934426018

Offset: 0

Author

Benoit Cloitre, Jan 26 2003

Keywords

• nonn
• changed

Comments

a(n) is the number of paths from (0,0) to (6n,n) taking north and east steps and avoiding north^{=2}. - Shanzhen Gao, Apr 15 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A052203.

Programs

Magma

[Binomial(6*n+1, n): n in [0..20]]; // Vincenzo Librandi, Aug 07 2014

Maple

seq(binomial(6*n+1,n), n = 1 .. 100); # Robert Israel, Aug 07 2014

Mathematica

Table[Binomial[6 n + 1, n], {n, 0, 20}] (* Vincenzo Librandi, Aug 07 2014 *)

Formula

a(n) is asymptotic to c*sqrt(n)*(46656/3125)^n with c= 0.5243... [c = 2*3^(3/2)/(5^(3/2)*sqrt(Pi)) = 0.52442324668419795386... - Vaclav Kotesovec, Feb 14 2019]

G.f.: hypergeom([1/3, 1/2, 2/3, 5/6, 7/6], [2/5, 3/5, 4/5, 6/5], (46656/3125)*x). - Robert Israel, Aug 07 2014