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A215298
Number of solid standard Young tableaux of shape [[n,n-2],[2]].
2
2, 25, 174, 962, 4804, 22689, 103510, 461318, 2021916, 8752042, 37520972, 159633060, 674969224, 2839400945, 11893509990, 49637986590, 206519808300, 856904298030, 3547095101220, 14652264350940, 60412895258040, 248675669866650, 1022088942267900, 4195255959533052
OFFSET
2,1
LINKS
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.
a(n) ~ 3 * 2^(2*n-1) * sqrt(n) / sqrt(Pi). - Vaclav Kotesovec, Sep 02 2014
a(n) = 12*(1 - 4*n + 10*n^2 - 8*n^3 + 2*n^4) * (2*n-4)! / ((n-2)! * (n+1)!). - Vaclav Kotesovec, Sep 02 2014
MAPLE
a:= proc(n) option remember; `if`(n=2, 2,
2*(4*n^5 -26*n^4 +60*n^3 -58*n^2 +22*n -5)*a(n-1)/
(2*n^5 -14*n^4 +30*n^3 -10*n^2 -31*n +25))
end:
seq(a(n), n=2..30);
MATHEMATICA
Table[12*(1 - 4*n + 10*n^2 - 8*n^3 + 2*n^4) * (2*n-4)! / ((n-2)! * (n+1)!), {n, 2, 20}] (* Vaclav Kotesovec, Sep 02 2014 *)
CROSSREFS
Column k=2 of A214775.
Cf. A215002.
Sequence in context: A024533 A220276 A361874 * A094218 A203767 A206392
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 07 2012
STATUS
approved