A288325 Number of Dyck paths of semilength n such that each positive level has exactly nine peaks.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 440, 6160, 40040, 140140, 280280, 320320, 194480, 48620, 0, 100, 9350, 382800, 9083800, 142638320, 1602400800, 13556342800, 89523519800, 473679520600, 2047398407340, 7334909697400, 22016582387800

Offset

0,20

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, 9$2)):
seq(a(n), n=0..42);

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, 9, 9]];
Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=9 of A288318.

Cf. A000108.

Sequence in context: A199835 A350565 A001327 * A222665 A177391 A304289

Adjacent sequences: A288322 A288323 A288324 * A288326 A288327 A288328

Keyword

nonn

Author

Alois P. Heinz, Jun 07 2017

Status

approved