A289479 Number of Dyck paths of semilength 9*n and height n.

1, 1, 131071, 53249182309, 24707711028329725, 10683679703096752747668, 4147304882800594101766257490, 1455763914060254648633279812633997, 470172045819740629127626302976354304026, 142143740345412121643458345045577780672138977

Offset: 0

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..186

Crossrefs

Column k=9 of A289481.

Programs

Maple

b:= proc(x, y, k) option remember;
      `if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+
      `if`(y <  min(x-1, k), b(x-1, y+1, k), 0))
    end:
a:= n-> `if`(n=0, 1, b(18*n, 0, n)-b(18*n, 0, n-1)):
seq(a(n), n=0..20);

Mathematica

b[x_, y_, k_]:=b[x, y, k]=If[x==0, 1, If[y>0, b[x - 1, y - 1, k], 0] + If[yIndranil Ghosh, Jul 07 2017, after Maple code *)

Formula

a(n) ~ 3^(36*n + 1) / (2^(16*n + 2)* 5^(10*n + 7/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017