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

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, 1009008, 1633632, 1575288, 831402, 184756, 0, 121, 13794, 686070, 19744296, 375698466, 5114697588, 52484019588, 421146343332, 2715042399498, 14352204442576

Offset

0,22

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Counting lattice paths

Maple

b:= proc(n, k, j) option remember;
     `if`(n=j, 1, add(b(n-j, k, i)*(binomial(i, k)
      *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))
    end:
a:= n-> `if`(n=0, 1, b(n, 10$2)):
seq(a(n), n=0..45);

Mathematica

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]}]];
a[n_] := If[n == 0, 1, b[n, 10, 10]];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=10 of A288318.

Cf. A000108.

Sequence in context: A265978 A263184 A370087 * A260583 A079915 A185656

Adjacent sequences: A288323 A288324 A288325 * A288327 A288328 A288329

Keyword

nonn

Author

Alois P. Heinz, Jun 07 2017

Status

approved