A289478 Number of Dyck paths of semilength 8*n and height n.

1, 1, 32767, 2962826465, 302279227822132, 28940151142665744800, 2518778621914294827210397, 200931623862007000173683722721, 14934414860406931133627906259665137, 1050339437420146526008731445371770861951, 70783666464470090848536562606347425026054174

Offset: 0

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..210

Crossrefs

Column k=8 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(16*n, 0, n)-b(16*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^(64*n + 9/2) / (3^(18*n + 7) * 7^(7*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017