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A215687 Number of solid standard Young tableaux of shape [[2*n,2],[2]]. 2

%I #18 Jul 19 2017 20:49:46

%S 0,16,174,690,1876,4140,7986,14014,22920,35496,52630,75306,104604,

%T 141700,187866,244470,312976,394944,492030,605986,738660,891996,

%U 1068034,1268910,1496856,1754200,2043366,2366874,2727340,3127476,3570090,4058086,4594464,5182320

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

%H Alois P. Heinz, <a href="/A215687/b215687.txt">Table of n, a(n) for n = 0..1000</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>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: 2*(3*x^3-10*x^2+47*x+8)*x/(1-x)^5.

%F a(n) = n*(2*n-1)*(2*n^2+7*n+7).

%p a:= n-> (-7+(7+(12+4*n)*n)*n)*n;

%p seq(a(n), n=0..40);

%t LinearRecurrence[{5,-10,10,-5,1},{0,16,174,690,1876},40] (* _Harvey P. Dale_, Jul 08 2017 *)

%Y Row n=2 of A176129.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Aug 20 2012

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)