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%I #11 Jan 09 2024 14:16:28
%S 1,44,891,11440,106964,787644,4803656,25126816,115640460,477409504,
%T 1794876116,6219677664,20060380120,60709045100,173556446580,
%U 471387879600,1222309899525,3038581131300,7268211039375,16781568991200,37505964810600,81340096523400
%N Dimensions of certain Lie algebra (see reference for precise definition).
%H Paolo Xausa, <a href="/A133349/b133349.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), pp. 143-179. [Th. 7.2(ii), case a = 6]
%p b:=binomial; t72b:= proc(a,k) ((a+k+1)/(a+1)) * b(k+2*a+1,k)*b(k+3*a/2+1,k)/(b(k+a/2,k)); end; [seq(t72b(6,k),k=0..28)];
%t t72b[a_, k_] := (a+k+1) / (a+1) Binomial[k+2a+1, k] Binomial[k+3/2a+1, k] / Binomial[k+a/2, k];
%t Array[t72b[6, #]&, 30, 0] (* _Paolo Xausa_, Jan 09 2024 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 20 2007
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