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Search: id:A128894
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| A128894 |
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Triangle read by rows, giving dimensions of exceptional groups with extension to E9 as a non-simple Lie Algebra. |
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+0
4
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| 3, 8, 27, 14, 77, 273, 28, 300, 1925, 8918, 52, 1053, 12376, 100776, 627912, 78, 2430, 43758, 537966, 4969107, 36685506, 133, 7371, 238602, 5248750, 85709988, 1101296924, 11604306012, 190, 15504, 749360, 24732110, 605537790, 11619550320
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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This result is all based on work originally by Deligne. Row Sum: Table[Apply[Plus, Table[g[a[[n]], k], {k, 1, n}]], {n, 1, Length[a]}]
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REFERENCES
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J. M. Landsberg, The sextonions and E_{7 1/2} (with L.Manivel) (Advances in Math 201(2006) p143 - 179) page 22
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [See Th. 7.1]
J. M. Landsberg, http : // www.math.tamu.edu/~jml/LMsexpub.pdf :The sextonions and E_{7 1/2}
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FORMULA
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a[a,k]= (3*a + 2*k + 5)*binomial[k + 2*a + 3, k]*binomial[k + 5*a/2 + 3, k]*binomial[k + 3*a + 4, k]/((3*a + 5)*binomial[k + a/2 + 1, k]*binomial[k + a + 1, k])
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EXAMPLE
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Triangle begins:
{3},
{8, 27},
{14, 77, 273},
{28, 300, 1925, 8918},
{52, 1053, 12376, 100776, 627912},
{78, 2430, 43758, 537966, 4969107, 36685506}
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MATHEMATICA
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Clear[a, g, k] (*http : // www.math.tamu.edu/~jml /: The sextonions and E_{7 1/2} (with L.Manivel) ( Advances in Math 201(2006) p143 - 179) : http : // www.math.tamu.edu/~jml/LMsexpub.pdf : page 22*) a = {-4/3, -1, -2/3, 0, 1, 2, 4, 6, 8, 16}; g[a_, k_] := (3*a + 2*k + 5)*Binomial[k + 2*a + 3, k]*Binomial[k + 5*a/2 + 3, k]*Binomial[k + 3*a + 4, k]/((3*a + 5)*Binomial[k + a/2 + 1, k]*Binomial[k + a + 1, k]) b = Table[Table[g[a[[n]], k], {k, 1, n}], {n, 1, Length[a]}]
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CROSSREFS
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Cf. A133238.
Adjacent sequences: A128891 A128892 A128893 this_sequence A128895 A128896 A128897
Sequence in context: A054097 A088590 A023637 this_sequence A118165 A066020 A066018
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 09 2007
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