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%I #16 Jan 10 2024 00:26:27
%S 1,27,351,3003,19305,100386,442442,1706562,5895396,18559580,53965548,
%T 146477916,374332452,907036326,2096092350,4642456390,9895762305,
%U 20373628275,40639459575,78751105875,148599912825,273612537900,492502568220,868056366060,1500344336400
%N Dimensions of multiples of minimal representation of complex Lie algebra E6.
%D Onishchik and Vinberg, Seminar on Lie Groups and Algebraic Groups, Springer Verlag 1990, see Table 5.
%H T. D. Noe, <a href="/A030648/b030648.txt">Table of n, a(n) for n = 0..1000</a>
%H J. M. Landsberg and L. Manivel, <a href="https://doi.org/10.1016/j.aim.2005.02.001">The sextonions and E7 1/2</a>, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=8]
%F a(n) = (1/517440)*binomial(n+11, 3)*binomial(n+3, 3)*binomial(n+8, 5)^2.
%p b:=binomial; t73:= proc(a,k) ((2*k+a)*(k+a)/(a^2)) * b(k+a-1,k)*b(k+3*a/2-1,k)/(b(k+a/2,k)); end; [seq(t73(8,k),k=0..40)];
%t Table[(Binomial[n+11,3]Binomial[n+3,3]Binomial[n+8,5]^2)/517440,{n,0,30}] (* _Harvey P. Dale_, May 01 2011 *)
%K nonn
%O 0,2
%A Paolo Dominici (pl.dm(AT)libero.it)
%E Edited by _N. J. A. Sloane_, Oct 20 2007
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