A030650 Dimensions of multiples of minimal representations of complex Lie algebra E_8.

248, 27000, 1763125, 79143000, 2642777280, 69176971200, 1473701482500, 26284473168750, 401283501480000, 5338265882241600, 62790857238950100, 661062273763905000, 6294003651511200000, 54675736068345120000

Offset: 1

Author

Paolo Dominici (pl.dm(AT)libero.it)

Keywords

• nonn

Comments

Dimensions of certain Lie algebra (see Landsberg-Manivel reference for precise definition). - N. J. A. Sloane, Oct 15 2007

References

• Cf. table 5 of Seminar on Lie Groups and Algebraic Groups of Onishchik and Vinberg [ Springer Verlag 1990 ].

Links

• J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=8]

Crossrefs

Cf. A121732.

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(8,k),k=0..30)]; # N. J. A. Sloane, Oct 15 2007

Formula

a(n) = (1/298109643686752257360)*(2*n+29)*binomial(n+28, 5)*binomial(n+19, 10)* binomial(n+5, 5)*binomial(n+23, 18)^2.