A133239 - OEIS

%I #12 Jan 11 2024 10:59:21

%S 1,78,2430,43758,537966,4969107,36685506,225961450,1198006524,

%T 5597569328,23474156784,89644484592,315415779120,1032380107812,

%U 3168537039954,9180278955210,25252641533405,66272502260250,166635797864250,402908157902250,939815697512250

%N Dimensions of certain Lie algebra (see reference for precise definition).

%H Paolo Xausa, <a href="/A133239/b133239.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=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(2,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[2,#]&,30,0] (* _Paolo Xausa_, Jan 11 2024 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 15 2007