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A288326 Number of Dyck paths of semilength n such that each positive level has exactly ten peaks.

%I A288326 #8 Jun 02 2018 10:37:40
%S A288326 1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,594,10296,84084,378378,
%T A288326 1009008,1633632,1575288,831402,184756,0,121,13794,686070,19744296,
%U A288326 375698466,5114697588,52484019588,421146343332,2715042399498,14352204442576
%N A288326 Number of Dyck paths of semilength n such that each positive level has exactly ten peaks.
%H A288326 Alois P. Heinz, <a href="/A288326/b288326.txt">Table of n, a(n) for n = 0..1000</a>
%H A288326 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path#Counting_lattice_paths">Counting lattice paths</a>
%p A288326 b:= proc(n, k, j) option remember;
%p A288326      `if`(n=j, 1, add(b(n-j, k, i)*(binomial(i, k)
%p A288326       *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))
%p A288326     end:
%p A288326 a:= n-> `if`(n=0, 1, b(n, 10$2)):
%p A288326 seq(a(n), n=0..45);
%t A288326 b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];
%t A288326 a[n_] := If[n == 0, 1, b[n, 10, 10]];
%t A288326 Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, Jun 02 2018, from Maple *)
%Y A288326 Column k=10 of A288318.
%Y A288326 Cf. A000108.
%K A288326 nonn
%O A288326 0,22
%A A288326 _Alois P. Heinz_, Jun 07 2017