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 A030650 Dimensions of multiples of minimal representations of complex Lie algebra E_8. 3
 248, 27000, 1763125, 79143000, 2642777280, 69176971200, 1473701482500, 26284473168750, 401283501480000, 5338265882241600, 62790857238950100, 661062273763905000, 6294003651511200000, 54675736068345120000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 Table of n, a(n) for n=1..14. J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=8] 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. 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 CROSSREFS Cf. A121732. Sequence in context: A327959 A178967 A030062 * A299831 A045254 A197349 Adjacent sequences: A030647 A030648 A030649 * A030651 A030652 A030653 KEYWORD nonn AUTHOR Paolo Dominici (pl.dm(AT)libero.it) STATUS approved

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Last modified February 27 19:09 EST 2024. Contains 370378 sequences. (Running on oeis4.)