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A030648
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Dimensions of multiples of minimal representation of complex Lie algebra E6.
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1
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1, 27, 351, 3003, 19305, 100386, 442442, 1706562, 5895396, 18559580, 53965548, 146477916, 374332452, 907036326, 2096092350, 4642456390, 9895762305, 20373628275, 40639459575, 78751105875, 148599912825, 273612537900, 492502568220, 868056366060, 1500344336400
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OFFSET
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0,2
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REFERENCES
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J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=8]
Onishchik and Vinberg, Seminar on Lie Groups and Algebraic Groups, Springer Verlag 1990, see Table 5.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = (1/517440)*binomial(n+11, 3)*binomial(n+3, 3)*binomial(n+8, 5)^2.
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MAPLE
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b:=binomial; t73:= proc(a, k) ((2*k+a)*(k+a)/(a^2)) * b(k+a-1, k)*b(k+3*a/2-1, k)/(b(k+a/2, k)); end; [seq(t73(8, k), k=0..40)];
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MATHEMATICA
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Table[(Binomial[n+11, 3]Binomial[n+3, 3]Binomial[n+8, 5]^2)/517440, {n, 0, 30}] (* Harvey P. Dale, May 01 2011 *)
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CROSSREFS
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Sequence in context: A202289 A010943 A022622 * A223278 A278091 A042410
Adjacent sequences: A030645 A030646 A030647 * A030649 A030650 A030651
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KEYWORD
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nonn
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it)
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EXTENSIONS
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Edited by N. J. A. Sloane, Oct 20 2007
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STATUS
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approved
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