A289475 Number of Dyck paths of semilength 5*n and height n.

1, 1, 511, 497845, 517884748, 517500496981, 492342898340494, 450205866074148509, 399858332322926629152, 347831920544342751131378, 298149337418229660486879546, 252909751775727886411508895575, 212950273659595164912087912232227

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..343

Formula

a(n) ~ 5^(10*n + 1/2) / (2^(4*n + 3/2) * 3^(6*n + 7/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 14 2017

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(10*n, 0, n)-b(10*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[y<Min[x - 1, k], b[x - 1, y + 1, k], 0]]; a[n_]:=a[n]=If[n==0, 1, b[10n, 0, n] - b[10n, 0, n - 1]]; Table[a[n], {n, 0, 20}] (* Indranil Ghosh, Jul 08 2017 *)

Crossrefs

Column k=5 of A289481.

Sequence in context: A022191 A069384 A069410 * A069436 A217915 A263167

Adjacent sequences: A289472 A289473 A289474 * A289476 A289477 A289478

Keyword

nonn

Author

Alois P. Heinz, Jul 06 2017

Status

approved