A133352 Dimensions of certain Lie algebra (see reference for precise definition).

1, 495, 55055, 2550548, 65493792, 1095915744, 13232722140, 123515648685, 935877829315, 5967356119725, 32906870606610, 160314212254560, 701733465072640, 2797750569360384, 10273887744211872, 35073296276201118, 112179553015334805, 338384405311947995

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(iii), case a = 4]

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(4, 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[4, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)

Crossrefs

Sequence in context: A055157 A027808 A104478 * A140913 A214555 A333756

Adjacent sequences: A133349 A133350 A133351 * A133353 A133354 A133355

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2007

Status

approved