A133241 Dimensions of certain Lie algebra (see reference for precise definition).

1, 190, 15504, 749360, 24732110, 605537790, 11619550320, 181746027600, 2386644625950, 26923893369075, 265762390788000, 2330056309932000, 18372187417457250, 131651129456894250, 865026329992488000, 5251754282090616000, 29657709797595709500, 156694210053607278000

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=6]

Formula

Sum_{n>=0} 1/a(n) = 10009905786409129566567137280*log(2)/12103 - 41814159764706590976000*zeta(3) - 744231335143727853104827096749123/1422973916. - 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(6, 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[6, #]&, 30, 0] (* Paolo Xausa, Jan 11 2024 *)

Crossrefs

Sequence in context: A223462 A184192 A263523 * A229903 A221386 A217225

Adjacent sequences: A133238 A133239 A133240 * A133242 A133243 A133244

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 15 2007

Status

approved