login
A133239
Dimensions of certain Lie algebra (see reference for precise definition).
2
1, 78, 2430, 43758, 537966, 4969107, 36685506, 225961450, 1198006524, 5597569328, 23474156784, 89644484592, 315415779120, 1032380107812, 3168537039954, 9180278955210, 25252641533405, 66272502260250, 166635797864250, 402908157902250, 939815697512250
OFFSET
0,2
LINKS
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=2]
MAPLE
b:=binomial; t71:= proc(a, k) ((3*a+2*k+5)/(3*a+5)) * b(k+2*a+3, k)*b(k+5*a/2+3, k)*b(k+3*a+4, k)/(b(k+a/2+1, k)*b(k+a+1, k)); end; [seq(t71(2, k), k=0..30)];
MATHEMATICA
t71[a_, k_] := (3a+2k+5) / (3a+5) Binomial[k+2a+3, k] Binomial[k+5/2a+3, k] Binomial[k+3a+4, k] / (Binomial[k+a/2+1, k] Binomial[k+a+1, k]);
Array[t71[2, #]&, 30, 0] (* Paolo Xausa, Jan 11 2024 *)
CROSSREFS
Sequence in context: A036524 A262063 A140934 * A210407 A146479 A017794
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 15 2007
STATUS
approved