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A133318
Dimensions of certain Lie algebra (see reference for precise definition).
1
1, 66, 1638, 23100, 222156, 1613898, 9447438, 46562373, 199377750, 759230472, 2617486872, 8284996512, 24347884704, 67041815400, 174263649912, 430295153574, 1014662410839, 2295243043170, 4999983023750, 10524366180900, 21467370424500, 42543097418250
OFFSET
0,2
LINKS
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), pp. 143-179. [Th. 7.2(i), case a = 4]
FORMULA
Empirical g.f.: (x +1)*(x^8 +47*x^7 +556*x^6 +2342*x^5 +3832*x^4 +2342*x^3 +556*x^2 +47*x +1) / (x -1)^18. - Colin Barker, Jul 27 2013
MAPLE
b:=binomial; t72a:= proc(a, k) ((2*a+2*k+1)/(2*a+1)) * b(k+3*a/2-1, k)*b(k+3*a/2+1, k)*b(k+2*a, k)/(b(k+a/2-1, k)*b(k+a/2+1, k)); end; [seq(t72a(4, k), k=0..40)];
MATHEMATICA
t72a[a_, k_] := (2k+2a+1) / (2a+1) Binomial[k+3/2a-1, k] Binomial[k+3/2a+1, k] Binomial[k+2a, k] / (Binomial[k+a/2-1, k] Binomial[k+a/2+1, k]);
Array[t72a[4, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)
CROSSREFS
Sequence in context: A279889 A241799 A269498 * A197645 A270847 A140925
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2007
STATUS
approved