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%I #8 Apr 04 2013 10:16:36
%S 3,8,14,28,52,78,133,190,248,484
%N Leading term in row n of triangle in A128894.
%C The building exceptional group symmetry sequence in Cartan notation is (Deligne-Landsberg): {A1,A2,G2,D4,F4,E6,E7,E7.5,E8,E9} E9 seems to be closer to an E9.5. For a universe which is E8 symmetry to have evolved, there had to be a metastable (explosive) higher energy/ higher temperature state E9.
%D J. M. Landsberg, The sextonions and E_{7 1/2} (with L.Manivel) (Advances in Math 201(2006) p143 - 179) page 22
%F T(a,n) =(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]}]; k=1 T[n,1]
%t (*A128894*) (*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[g[a[[n]], 1], {n, 1, Length[a]}]
%Y Cf. A128894, A109161, A129024, A129025.
%K nonn,fini,full,uned
%O 1,1
%A _Roger L. Bagula_, May 11 2007
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