A289477 Number of Dyck paths of semilength 7*n and height n.

1, 1, 8191, 164531565, 3673214880049, 77462600751077244, 1505240258416480353423, 27202373147496127842409429, 464106749942563876038980247765, 7576947003340172511554825394061140, 119634586370431286462528705183632896422

Offset: 0

Author

Alois P. Heinz, Jul 06 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..241

Crossrefs

Column k=7 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(14*n, 0, n)-b(14*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) ~ 7^(14*n + 1/2) / (2^(16*n + 8) * 3^(6*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017