A133318 Dimensions of certain Lie algebra (see reference for precise definition).

1, 66, 1638, 23100, 222156, 1613898, 9447438, 46562373, 199377750, 759230472, 2617486872, 8284996512, 24347884704, 67041815400, 174263649912, 430295153574, 1014662410839, 2295243043170, 4999983023750, 10524366180900, 21467370424500, 42543097418250

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(i), case a = 4]

Formula

Empirical g.f.: (x +1)*(x^8 +47*x^7 +556*x^6 +2342*x^5 +3832*x^4 +2342*x^3 +556*x^2 +47*x +1) / (x -1)^18. - Colin Barker, Jul 27 2013

Maple

b:=binomial; t72a:= proc(a, k) ((2*a+2*k+1)/(2*a+1)) * b(k+3*a/2-1, k)*b(k+3*a/2+1, k)*b(k+2*a, k)/(b(k+a/2-1, k)*b(k+a/2+1, k)); end; [seq(t72a(4, k), k=0..40)];

Mathematica

t72a[a_, k_] := (2k+2a+1) / (2a+1) Binomial[k+3/2a-1, k] Binomial[k+3/2a+1, k] Binomial[k+2a, k] / (Binomial[k+a/2-1, k] Binomial[k+a/2+1, k]);
Array[t72a[4, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *)

Crossrefs

Sequence in context: A279889 A241799 A269498 * A197645 A270847 A140925

Adjacent sequences: A133315 A133316 A133317 * A133319 A133320 A133321

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2007

Status

approved