A133240 Dimensions of certain Lie algebra (see reference for precise definition).

1, 133, 7371, 238602, 5248750, 85709988, 1101296924, 11604306012, 103402141164, 797856027500, 5431803835220, 33125614508610, 183226228734150, 928793118827175, 4352687787515625, 18999500104801125, 77742635367237750, 299864450702202750

Offset

0,2

Links

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

Joseph M. Landsberg and Laurent Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=4; Th. 7.2(i), case a = 4]

Formula

Sum_{n>=0} 1/a(n) = 431192642722960769024*log(2)/675 - 32039798774151168*zeta(3) - 1117456880942087556297716/2764125. - Amiram Eldar, Jun 16 2026

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(4, 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[4, #]&, 30, 0] (* Paolo Xausa, Jan 11 2024 *)

Crossrefs

Sequence in context: A028295 A262121 A254684 * A129050 A129049 A281496

Adjacent sequences: A133237 A133238 A133239 * A133241 A133242 A133243

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 15 2007

Status

approved