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%I #10 Jul 14 2017 08:07:37
%S 1,1,2047,9096393,44100374341,203421120941736,877820839402932499,
%T 3578930527547615106601,13968353507597683646018640,
%U 52773530288643811045085269442,194648265795425910705859329140951,705285559217587334571033534680055625
%N Number of Dyck paths of semilength 6*n and height n.
%H Alois P. Heinz, <a href="/A289476/b289476.txt">Table of n, a(n) for n = 0..283</a>
%F a(n) ~ 2^(24*n + 7/2) * 3^(12*n + 1/2) / (5^(5*n+1/2) * 7^(7*n+7/2) * sqrt(Pi*n)). - _Vaclav Kotesovec_, Jul 14 2017
%p b:= proc(x, y, k) option remember;
%p `if`(x=0, 1, `if`(y>0, b(x-1, y-1, k), 0)+
%p `if`(y < min(x-1, k), b(x-1, y+1, k), 0))
%p end:
%p a:= n-> `if`(n=0, 1, b(12*n, 0, n)-b(12*n, 0, n-1)):
%p seq(a(n), n=0..20);
%t 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[12n, 0, n] - b[12n, 0, n - 1]]; Table[a[n], {n, 0, 20}] (* _Indranil Ghosh_, Jul 07 2017, after Maple code *)
%Y Column k=6 of A289481.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 06 2017
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