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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).

From Vaclav Kotesovec, Mar 26 2018: (Start)

Recurrence: 3*n*(3*n + 1)*(3*n + 2)*(3*n^3 - 11*n^2 + 10*n - 3)*a(n) =  - 24*(2*n - 1)*(6*n^3 - 1)*a(n-1) + 64*(n-1)*(2*n - 3)*(2*n - 1)*(3*n^3 - 2*n^2 - 3*n - 1)*a(n-2).

a(n) ~ ((3+2*sqrt(3)) - (-1)^n*(3-2*sqrt(3))) * 2^(4*n + 1) / (sqrt(Pi*n) * 3^(3*n/2 + 2)). (End)

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 A303204 A032203

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 May 26 13:30 EDT 2018. Contains 304608 sequences. (Running on oeis4.)