A288117 Number of Dyck paths of semilength n such that each level has exactly ten peaks or no peaks.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 46, 139, 337, 760, 1672, 3511, 6904, 12782, 22627, 39318, 75538, 207881, 812507, 3841220, 20378041, 105202200, 477568717, 1875871984, 6503542301, 20447457784, 59755535440, 165351799936, 437965172476, 1115247676801

Offset

0,13

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(j-1, i-1)+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..40);

Mathematica

b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[j - 1, i - 1] + 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, 40}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=10 of A288108.

Sequence in context: A320697 A081583 A244246 * A213834 A241084 A106600

Adjacent sequences: A288114 A288115 A288116 * A288118 A288119 A288120

Keyword

nonn

Author

Alois P. Heinz, Jun 05 2017

Status

approved