A133239 Dimensions of certain Lie algebra (see reference for precise definition).

1, 78, 2430, 43758, 537966, 4969107, 36685506, 225961450, 1198006524, 5597569328, 23474156784, 89644484592, 315415779120, 1032380107812, 3168537039954, 9180278955210, 25252641533405, 66272502260250, 166635797864250, 402908157902250, 939815697512250

Offset: 0

Author

N. J. A. Sloane, Oct 15 2007

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=2]

Programs

Maple

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)];

Mathematica

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]);
Array[t71[2,#]&,30,0] (* Paolo Xausa, Jan 11 2024 *)