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A288321 Number of Dyck paths of semilength n such that each positive level has exactly five peaks. 2
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 84, 336, 504, 252, 0, 36, 1134, 15960, 130536, 700560, 2639952, 7260840, 14894712, 23151996, 29957760, 60579792, 319505760, 1930565232, 9852185196, 41993000532, 151747572312, 471322972512, 1275430904496, 3072333948480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

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, 5$2)):

seq(a(n), n=0..35);

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, 5, 5]];

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Jun 02 2018, from Maple *)

CROSSREFS

Column k=5 of A288318.

Cf. A000108.

Sequence in context: A196256 A230491 A067249 * A155191 A211171 A054605

Adjacent sequences:  A288318 A288319 A288320 * A288322 A288323 A288324

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 07 2017

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)