A289476 Number of Dyck paths of semilength 6*n and height n.

1, 1, 2047, 9096393, 44100374341, 203421120941736, 877820839402932499, 3578930527547615106601, 13968353507597683646018640, 52773530288643811045085269442, 194648265795425910705859329140951, 705285559217587334571033534680055625

Offset: 0

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..283

Crossrefs

Column k=6 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(12*n, 0, n)-b(12*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) ~ 2^(24*n + 7/2) * 3^(12*n + 1/2) / (5^(5*n+1/2) * 7^(7*n+7/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017