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 A215688 Number of solid standard Young tableaux of shape [[3*n,3],[3]]. 2

%I #12 Jul 19 2017 20:50:19

%S 0,192,7020,52808,229680,738192,1950512,4488180,9314448,17841200,

%T 32050452,54630432,89126240,140105088,213336120,315984812,456821952,

%U 646447200,897527228,1225048440,1646584272,2182577072,2856634560,3695840868,4731082160,5997386832

%N Number of solid standard Young tableaux of shape [[3*n,3],[3]].

%H Alois P. Heinz, <a href="/A215688/b215688.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>

%F G.f.: 4*(8*x^6-41*x^5+105*x^4+181*x^3+1925*x^2+1419*x+48)*x/(1-x)^7.

%F a(n) = (3*n-1)*(3*n-2)*(3*n^2+13*n+16)*(3*n^2+5*n+4)/4 for n>0, a(0) = 0.

%p a:= n-> `if`(n=0, 0, 32+(-312+(-362+(171+(657+(405+81*n)*n)*n)*n)*n)*n/4):

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

%Y Row n=3 of A176129.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Aug 20 2012

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Last modified August 7 20:39 EDT 2024. Contains 375017 sequences. (Running on oeis4.)