A215298 - OEIS

%I #16 Jul 19 2017 20:45:09

%S 2,25,174,962,4804,22689,103510,461318,2021916,8752042,37520972,

%T 159633060,674969224,2839400945,11893509990,49637986590,206519808300,

%U 856904298030,3547095101220,14652264350940,60412895258040,248675669866650,1022088942267900,4195255959533052

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

%H Alois P. Heinz, <a href="/A215298/b215298.txt">Table of n, a(n) for n = 2..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 a(n) ~ 3 * 2^(2*n-1) * sqrt(n) / sqrt(Pi). - _Vaclav Kotesovec_, Sep 02 2014

%F 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 a:= proc(n) option remember; `if`(n=2, 2,

%p       2*(4*n^5 -26*n^4 +60*n^3 -58*n^2 +22*n -5)*a(n-1)/

%p         (2*n^5 -14*n^4 +30*n^3 -10*n^2 -31*n +25))

%p     end:

%p seq(a(n), n=2..30);

%t 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 Column k=2 of A214775.

%Y Cf. A215002.

%K nonn

%O 2,1

%A _Alois P. Heinz_, Aug 07 2012