cp's OEIS Frontend

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

%I A215688 #12 Jul 19 2017 20:50:19
%S A215688 0,192,7020,52808,229680,738192,1950512,4488180,9314448,17841200,
%T A215688 32050452,54630432,89126240,140105088,213336120,315984812,456821952,
%U A215688 646447200,897527228,1225048440,1646584272,2182577072,2856634560,3695840868,4731082160,5997386832
%N A215688 Number of solid standard Young tableaux of shape [[3*n,3],[3]].
%H A215688 Alois P. Heinz, <a href="/A215688/b215688.txt">Table of n, a(n) for n = 0..1000</a>
%H A215688 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 A215688 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A215688 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 A215688 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 A215688 a:= n-> `if`(n=0, 0, 32+(-312+(-362+(171+(657+(405+81*n)*n)*n)*n)*n)*n/4):
%p A215688 seq(a(n), n=0..40);
%Y A215688 Row n=3 of A176129.
%K A215688 nonn
%O A215688 0,2
%A A215688 _Alois P. Heinz_, Aug 20 2012