A289473 Number of Dyck paths of semilength 3*n and height n.

1, 1, 31, 1341, 59917, 2665884, 117939506, 5201391077, 229151753951, 10097407871079, 445314691051823, 19662213285986440, 869281482750346782, 38482251447081815180, 1705762097183926444500, 75702251155478791228341, 3363573441149092994645423

Offset: 0

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..604

Crossrefs

Column k=3 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(6*n, 0, n)-b(6*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 08 2017 *)

Formula

a(n) ~ 3^(6*n + 1/2) / (2^(4*n + 9/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017