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A215300 Number of solid standard Young tableaux of shape [[n,n-4],[4]].

%I A215300 #15 Jul 19 2017 20:48:23
%S A215300 14,378,4804,43573,325590,2149454,13054108,74688594,408634828,
%T A215300 2159302420,11097147528,55747502501,274790652518,1332928973766,
%U A215300 6377276361900,30149660760870,141057202034340,653892592144620,3006490865152440,13722387184879650,62220533305358076
%N A215300 Number of solid standard Young tableaux of shape [[n,n-4],[4]].
%H A215300 Alois P. Heinz, <a href="/A215300/b215300.txt">Table of n, a(n) for n = 4..500</a>
%H A215300 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 A215300 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A215300 See Maple program.
%F A215300 For n > 4, a(n) = (2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567 + 2394*n - 8862*n^2 + 15592*n^3 - 15484*n^4 + 9152*n^5 - 3292*n^6 + 704*n^7 - 82*n^8 + 4*n^9)). - _Vaclav Kotesovec_, Sep 02 2014
%p A215300 a:= proc(n) option remember; `if`(n<6, [0$3, 14, 378, 4804][n],
%p A215300       ((-460961029024*n^4 +54902186125572*n^3 -347074341314956*n^2
%p A215300        +421934757637074*n +6838164520124) *a(n-1) +(104238656896016*n^4
%p A215300        -2317913124589048*n^3 +16535317231755832*n^2 -44274446438628908*n
%p A215300        +29901662719961532)*a(n-2) +(-391233321452352*n^4
%p A215300        +7447800734464704*n^3 -48294258553516272*n^2 +122447135865649584*n
%p A215300        -105955729051546080)*a(n-3)) / (286655151052*n^4 -1210962058579*n^3
%p A215300        +4322649356693*n^2 -24951473774234*n -30771740340558))
%p A215300     end:
%p A215300 seq(a(n), n=4..30);
%t A215300 Flatten[{14,Table[(2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567+2394*n-8862*n^2+15592*n^3-15484*n^4+9152*n^5-3292*n^6+704*n^7-82*n^8+4*n^9)),{n,5,20}]}] (* _Vaclav Kotesovec_, Sep 02 2014 *)
%Y A215300 Column k=4 of A214775.
%Y A215300 Cf. A215002.
%K A215300 nonn
%O A215300 4,1
%A A215300 _Alois P. Heinz_, Aug 07 2012