A133241 Dimensions of certain Lie algebra (see reference for precise definition).

1, 190, 15504, 749360, 24732110, 605537790, 11619550320, 181746027600, 2386644625950, 26923893369075, 265762390788000, 2330056309932000, 18372187417457250, 131651129456894250, 865026329992488000, 5251754282090616000, 29657709797595709500, 156694210053607278000

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=6]

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(6,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[6, #]&, 30, 0] (* Paolo Xausa, Jan 11 2024 *)