A288323 Number of Dyck paths of semilength n such that each positive level has exactly seven peaks.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 8, 216, 1800, 6600, 11880, 10296, 3432, 0, 64, 3744, 96768, 1454160, 14460480, 102586176, 544817856, 2237725512, 7268659712, 18954982080, 40057015680, 68941928016, 97350892224, 122456030112, 244967552640

Offset

0,16

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, 7$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, 7, 7]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 02 2018, from Maple *)

Crossrefs

Column k=7 of A288318.

Cf. A000108.

Sequence in context: A334582 A195506 A069045 * A264056 A271400 A123057

Adjacent sequences: A288320 A288321 A288322 * A288324 A288325 A288326

Keyword

nonn

Author

Alois P. Heinz, Jun 07 2017

Status

approved