This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289473 #13 Jul 14 2017 06:50:35
%S A289473 1,1,31,1341,59917,2665884,117939506,5201391077,229151753951,
%T A289473 10097407871079,445314691051823,19662213285986440,869281482750346782,
%U A289473 38482251447081815180,1705762097183926444500,75702251155478791228341,3363573441149092994645423
%N A289473 Number of Dyck paths of semilength 3*n and height n.
%H A289473 Alois P. Heinz, <a href="/A289473/b289473.txt">Table of n, a(n) for n = 0..604</a>
%F A289473 a(n) ~ 3^(6*n + 1/2) / (2^(4*n + 9/2) * sqrt(Pi*n)). - _Vaclav Kotesovec_, Jul 14 2017
%p A289473 b:= proc(x, y, k) option remember;
%p A289473 `if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+
%p A289473 `if`(y < min(x-1, k), b(x-1, y+1, k), 0))
%p A289473 end:
%p A289473 a:= n-> `if`(n=0, 1, b(6*n, 0, n)-b(6*n, 0, n-1)):
%p A289473 seq(a(n), n=0..20);
%t A289473 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[6n, 0, n] - b[6n, 0, n - 1]]; Table[a[n], {n, 0, 20}] (* _Indranil Ghosh_, Jul 08 2017 *)
%Y A289473 Column k=3 of A289481.
%K A289473 nonn
%O A289473 0,3
%A A289473 _Alois P. Heinz_, Jul 06 2017