A288322 Number of Dyck paths of semilength n such that each positive level has exactly six peaks.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 7, 140, 840, 2100, 2310, 924, 0, 49, 2156, 42140, 479220, 3598560, 19184676, 75954564, 229873063, 541427264, 1002386336, 1473318476, 1876489398, 3785310858, 20726607804, 136977861097, 786065454860, 3841493284076

Offset

0,14

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, 6$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[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];
a[n_] := If[n == 0, 1, b[n, 6, 6]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=6 of A288318.

Cf. A000108.

Sequence in context: A280629 A348188 A238692 * A297650 A085708 A054606

Adjacent sequences: A288319 A288320 A288321 * A288323 A288324 A288325

Keyword

nonn

Author

Alois P. Heinz, Jun 07 2017

Status

approved