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A133354
Dimensions of certain Lie algebra (see reference for precise definition).
1
1, 1539, 617253, 105489615, 9743909175, 561104814270, 22155294211050, 641798777779380, 14341812253735200, 256924158460700640, 3803151504372077088, 47661484991340720864, 515805481647912249276, 4900345026363722587050, 41434653012551675362750, 315469600749446851604325
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(iii), case a = 8]
MAPLE
b:=binomial; t72c:= proc(a, k) ((4*k+3*a+2)/((3*a+2)*(k+1))) * b(k+a, k)*b(k+a+1, k)*b(k+3*a/2-1, k)*b(k+3*a/2, k)*b(2*k+2*a+1, 2*k)/ (b(k+a/2-1, k)*b(k+a/2, k)*b(2*k+a, 2*k)); end; [seq(t72c(8, k), k=0..40)];
MATHEMATICA
t72c[a_, k_] := (4k+3a+2) / ((k+1)(3a+2)) Binomial[k+a, k] Binomial[k+a+1, k] Binomial[k+3/2a-1, k] Binomial[k+3/2a, k] Binomial[2k+2a+1, 2k] / (Binomial[k+a/2-1, k] Binomial[k+a/2, k] Binomial[2k+a, 2k]);
Array[t72c[8, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)
CROSSREFS
Sequence in context: A223377 A282543 A202166 * A283900 A104167 A237400
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2007
STATUS
approved