|
|
A288323
|
|
Number of Dyck paths of semilength n such that each positive level has exactly seven peaks.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,16
|
|
LINKS
|
|
|
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]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|