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A215298 Number of solid standard Young tableaux of shape [[n,n-2],[2]].

%I A215298 #16 Jul 19 2017 20:45:09
%S A215298 2,25,174,962,4804,22689,103510,461318,2021916,8752042,37520972,
%T A215298 159633060,674969224,2839400945,11893509990,49637986590,206519808300,
%U A215298 856904298030,3547095101220,14652264350940,60412895258040,248675669866650,1022088942267900,4195255959533052
%N A215298 Number of solid standard Young tableaux of shape [[n,n-2],[2]].
%H A215298 Alois P. Heinz, <a href="/A215298/b215298.txt">Table of n, a(n) for n = 2..500</a>
%H A215298 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 A215298 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A215298 See Maple program.
%F A215298 a(n) ~ 3 * 2^(2*n-1) * sqrt(n) / sqrt(Pi). - _Vaclav Kotesovec_, Sep 02 2014
%F A215298 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
%p A215298 a:= proc(n) option remember; `if`(n=2, 2,
%p A215298       2*(4*n^5 -26*n^4 +60*n^3 -58*n^2 +22*n -5)*a(n-1)/
%p A215298         (2*n^5 -14*n^4 +30*n^3 -10*n^2 -31*n +25))
%p A215298     end:
%p A215298 seq(a(n), n=2..30);
%t A215298 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 *)
%Y A215298 Column k=2 of A214775.
%Y A215298 Cf. A215002.
%K A215298 nonn
%O A215298 2,1
%A A215298 _Alois P. Heinz_, Aug 07 2012