A133319 Dimensions of certain Lie algebra (see reference for precise definition).

1, 99, 3927, 89661, 1387386, 15991118, 146005860, 1102439052, 7104607224, 40026446824, 200870048808, 911470725816, 3785393728644, 14533745396940, 52021580746190, 174825979846650, 554970843001575, 1672767047791125, 4809070448807625, 13239084661963875

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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 = 6]

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(6, 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[6, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)

Crossrefs

Sequence in context: A246247 A157370 A163040 * A196745 A196903 A017815

Adjacent sequences: A133316 A133317 A133318 * A133320 A133321 A133322

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2007

Status

approved