|
%I #15 Jan 10 2024 00:26:36
%S 248,27000,1763125,79143000,2642777280,69176971200,1473701482500,
%T 26284473168750,401283501480000,5338265882241600,62790857238950100,
%U 661062273763905000,6294003651511200000,54675736068345120000
%N Dimensions of multiples of minimal representations of complex Lie algebra E_8.
%C Dimensions of certain Lie algebra (see Landsberg-Manivel reference for precise definition). - _N. J. A. Sloane_, Oct 15 2007
%D Cf. table 5 of Seminar on Lie Groups and Algebraic Groups of Onishchik and Vinberg [ Springer Verlag 1990 ].
%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. 7.1, case a=8]
%F a(n) = (1/298109643686752257360)*(2*n+29)*binomial(n+28, 5)*binomial(n+19, 10)* binomial(n+5, 5)*binomial(n+23, 18)^2.
%p b:=binomial; t71:= proc(a,k) ((3*a+2*k+5)/(3*a+5)) * b(k+2*a+3,k)*b(k+5*a/2+3,k)*b(k+3*a+4,k)/(b(k+a/2+1,k)*b(k+a+1,k)); end; [seq(t71(8,k),k=0..30)]; # _N. J. A. Sloane_, Oct 15 2007
%Y Cf. A121732.
%K nonn
%O 1,1
%A Paolo Dominici (pl.dm(AT)libero.it)
|
