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%I #13 Jul 19 2017 20:46:06
%S 5,98,962,7020,43573,245962,1305238,6633172,32649890,156817044,
%T 738717796,3425580376,15679951989,70992594650,318450985230,
%U 1417072222020,6261985407990,27502477286460,120137081521500,522256720264680,2260525598620770,9746264904755652
%N Number of solid standard Young tableaux of shape [[n,n-3],[3]].
%H Alois P. Heinz, <a href="/A215299/b215299.txt">Table of n, a(n) for n = 3..500</a>
%H S. B. Ekhad, D. Zeilberger, <a href="https://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229v1 [math.CO], 2012
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F See Maple program.
%F 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
%p a:= proc(n) option remember; `if`(n<5, [0$2, 5, 98][n],
%p 2*(32*n^7 -400*n^6 +1976*n^5 -4900*n^4 +6452*n^3 -4420*n^2
%p +1350*n-315)*a(n-1) / (16*n^7 -224*n^6 +1204*n^5 -3008*n^4
%p +2980*n^3 +1072*n^2 -4155*n +2205))
%p end:
%p seq(a(n), n=3..30);
%t 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 *)
%Y Column k=3 of A214775.
%Y Cf. A215002.
%K nonn
%O 3,1
%A _Alois P. Heinz_, Aug 07 2012
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