

A288324


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


2



1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 315, 3465, 17325, 45045, 63063, 45045, 12870, 0, 81, 6075, 200340, 3835755, 48617415, 440531784, 3000152925, 15896972520, 67174514550, 230430986514, 649879542063, 1519950287430, 2963421671535, 4828750295985
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OFFSET

0,18


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(nj, k, i)*(binomial(i, k)
*binomial(j1, i1k)), i=1..min(j+k, nj)))
end:
a:= n> `if`(n=0, 1, b(n, 8$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, 8, 8]];
Table[a[n], {n, 0, 40}] (* JeanFrançois Alcover, Jun 02 2018, from Maple *)


CROSSREFS

Column k=8 of A288318.
Cf. A000108.
Sequence in context: A160194 A217145 A266835 * A317634 A198401 A135609
Adjacent sequences: A288321 A288322 A288323 * A288325 A288326 A288327


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Jun 07 2017


STATUS

approved



