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A288112
Number of Dyck paths of semilength n such that each level has exactly five peaks or no peaks.
2
1, 0, 0, 0, 0, 1, 1, 5, 11, 19, 32, 60, 178, 612, 1910, 6505, 22097, 62717, 155341, 365413, 908850, 2587326, 8337462, 28613490, 99865122, 341887279, 1112148217, 3385839203, 9723179369, 27116765041, 76656520298, 228493968174, 728697760582, 2447359432110
OFFSET
0,8
LINKS
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, 5$2)):
seq(a(n), n=0..37);
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, 5, 5]];
Table[a[n], {n, 0, 37}] (* Jean-François Alcover, Jun 02 2018, from Maple *)
CROSSREFS
Column k=5 of A288108.
Sequence in context: A125003 A062718 A326123 * A225250 A105914 A289530
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2017
STATUS
approved