A133353 Dimensions of certain Lie algebra (see reference for precise definition).

1, 945, 219912, 21488544, 1139660280, 38177564139, 892057462725, 15580701253260, 213956841238140, 2399777401421400, 22644486186626304, 184024677027809280, 1312566991805977344, 8344965320236093032, 47903608753899166620, 250980634154501770596

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), pp. 143-179. [Th. 7.2(iii), case a = 6]

Formula

Sum_{n>=0} 1/a(n) = 8992714461549434950321/2970 - 269588925178773200*Pi^2 - 3434179311763200*Pi^4 - 33902668800000*Pi^6. - Amiram Eldar, Jun 16 2026

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

Crossrefs

Sequence in context: A289953 A112491 A263889 * A322252 A351806 A119240

Adjacent sequences: A133350 A133351 A133352 * A133354 A133355 A133356

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 20 2007

Status

approved