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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Cf. A282869, A283667.

Sequence in context: A055192 A108555 A292169 * A225798 A032203 A197444

Adjacent sequences:  A283796 A283797 A283798 * A283800 A283801 A283802

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 16 2017

STATUS

approved

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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)