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A030648 Dimensions of multiples of minimal representation of complex Lie algebra E6. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (1/517440)*binomial(n+11, 3)*binomial(n+3, 3)*binomial(n+8, 5)^2.

MAPLE

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)];

MATHEMATICA

Table[(Binomial[n+11, 3]Binomial[n+3, 3]Binomial[n+8, 5]^2)/517440, {n, 0, 30}] (* Harvey P. Dale, May 01 2011 *)

CROSSREFS

Sequence in context: A202289 A010943 A022622 * A223278 A278091 A042410

Adjacent sequences: A030645 A030646 A030647 * A030649 A030650 A030651

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Edited by N. J. A. Sloane, Oct 20 2007

STATUS

approved

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Last modified February 3 10:55 EST 2023. Contains 360034 sequences. (Running on oeis4.)