A133240 Dimensions of certain Lie algebra (see reference for precise definition).

1, 133, 7371, 238602, 5248750, 85709988, 1101296924, 11604306012, 103402141164, 797856027500, 5431803835220, 33125614508610, 183226228734150, 928793118827175, 4352687787515625, 18999500104801125, 77742635367237750, 299864450702202750

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=4; Th. 7.2(i), case a = 4]

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(4,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[4,#]&,30,0] (* Paolo Xausa, Jan 11 2024 *)