A133350 Dimensions of certain Lie algebra (see reference for precise definition).

1, 90, 1274, 8568, 38115, 130130, 369460, 915552, 2043621, 4198810, 8065134, 14651000, 25393095, 42280434, 68000360, 106108288, 161222985, 239249178, 347629282, 495626040, 694637867, 958548690, 1304114076, 1751385440, 2324174125, 3050557146, 3963426390

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 = 1]

Formula

Empirical g.f.: (14*x^5+273*x^4+840*x^3+582*x^2+82*x+1) / (x-1)^8. - Colin Barker, Jul 27 2013

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(1, 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[1, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)

Crossrefs

Sequence in context: A213455 A155016 A179800 * A279438 A250869 A234983

Adjacent sequences: A133347 A133348 A133349 * A133351 A133352 A133353

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2007

Status

approved