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A215299 Number of solid standard Young tableaux of shape [[n,n-3],[3]]. 2
5, 98, 962, 7020, 43573, 245962, 1305238, 6633172, 32649890, 156817044, 738717796, 3425580376, 15679951989, 70992594650, 318450985230, 1417072222020, 6261985407990, 27502477286460, 120137081521500, 522256720264680, 2260525598620770, 9746264904755652 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..500

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012

Wikipedia, Young tableau

FORMULA

See Maple program.

For n > 3, a(n) = (8*(45 - 180*n + 580*n^2 - 756*n^3 + 484*n^4 - 144*n^5 + 16*n^6) * (2*n-6)!) / (3 * (n-3)! * (n+1)!). - Vaclav Kotesovec, Sep 02 2014

MAPLE

a:= proc(n) option remember; `if`(n<5, [0$2, 5, 98][n],

      2*(32*n^7 -400*n^6 +1976*n^5 -4900*n^4 +6452*n^3 -4420*n^2

      +1350*n-315)*a(n-1) / (16*n^7 -224*n^6 +1204*n^5 -3008*n^4

      +2980*n^3 +1072*n^2 -4155*n +2205))

    end:

seq(a(n), n=3..30);

MATHEMATICA

Flatten[{5, Table[(8*(45 - 180*n + 580*n^2 - 756*n^3 + 484*n^4 - 144*n^5 + 16*n^6) * (2*n-6)!) / (3*(n-3)!*(n+1)!), {n, 4, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

CROSSREFS

Column k=3 of A214775.

Cf. A215002.

Sequence in context: A202516 A062538 A053980 * A088995 A093749 A197474

Adjacent sequences:  A215296 A215297 A215298 * A215300 A215301 A215302

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 07 2012

STATUS

approved

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Last modified May 25 11:04 EDT 2019. Contains 323539 sequences. (Running on oeis4.)