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A283799 revision #3

A283799
Number of dispersed Dyck prefixes of length 2n and height n.
3
1, 2, 5, 12, 36, 90, 286, 728, 2380, 6120, 20349, 52668, 177100, 460460, 1560780, 4071600, 13884156, 36312408, 124403620, 326023280, 1121099408, 2942885946, 10150595910, 26681566392, 92263734836, 242799302200, 841392966470, 2216352204360, 7694644696200
OFFSET
0,2
FORMULA
Recursion: see Maple program.
a(n) = A282869(2n,n).
MAPLE
a:= proc(n) option remember; `if`(n<3, 1+n^2, ((512*(2*n-5))
*(2519*n-1279)*(n-2)*(2*n-3)*a(n-3) +(192*(2*n-3))
*(1710*n^3-443*n^2-4990*n+2483)*a(n-2) -(24*(22671*n^4
-124866*n^3+216436*n^2-129032*n+24526))*a(n-1))
/ ((3*n+2)*(27*n+9)*(855*n-1504)*n))
end:
seq(a(n), n=0..30);
CROSSREFS
Sequence in context: A108555 A323397 A292169 * A225798 A303204 A333411
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 16 2017
STATUS
editing