A133351 Dimensions of certain Lie algebra (see reference for precise definition).

1, 189, 6720, 103125, 945945, 6117748, 30707712, 127152180, 452615625, 1426106605, 4063625280, 10643113845, 25946898705, 59468850000, 129170145280, 267637365072, 531858496113, 1018308094245, 1885647400000, 3388127079645, 5923761615849, 10102561208916

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 = 2]

Formula

Empirical g.f.: -(x +1)*(x^8 +175*x^7 +4166*x^6 +26055*x^5 +50086*x^4 +26055*x^3 +4166*x^2 +175*x +1) / (x -1)^13. - 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(2, 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[2, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)

Crossrefs

Sequence in context: A297229 A211819 A266135 * A267993 A286791 A076012

Adjacent sequences: A133348 A133349 A133350 * A133352 A133353 A133354

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2007

Status

approved