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%I #12 Jan 11 2024 11:00:17
%S 1,133,7371,238602,5248750,85709988,1101296924,11604306012,
%T 103402141164,797856027500,5431803835220,33125614508610,
%U 183226228734150,928793118827175,4352687787515625,18999500104801125,77742635367237750,299864450702202750
%N Dimensions of certain Lie algebra (see reference for precise definition).
%H Paolo Xausa, <a href="/A133240/b133240.txt">Table of n, a(n) for n = 0..10000</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. 7.1, case a=4; Th. 7.2(i), case a = 4]
%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(4,k),k=0..30)];
%t t71[a_, k_] := (3a+2k+5) / (3a+5) Binomial[k+2a+3,k] Binomial[k+5/2a+3,k] Binomial[k+3a+4,k] / (Binomial[k+a/2+1,k] Binomial[k+a+1,k]);
%t Array[t71[4,#]&,30,0] (* _Paolo Xausa_, Jan 11 2024 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 15 2007