login
A133355
Dimensions of certain Lie algebra (see reference for precise definition).
1
1, 21, 210, 1386, 6930, 28314, 99099, 306735, 858858, 2212210, 5309304, 11992344, 25697880, 52581816, 103285710, 195635286, 358664691, 638489775, 1106715610, 1872263250, 3097744650, 5021809650, 7989242625, 12491007165, 19216934100, 29124331236, 43526473056
OFFSET
0,2
LINKS
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, arXiv:math/0402157 [math.RT], 2004-2005.
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=6]
FORMULA
Empirical g.f.: (x^4+8*x^3+15*x^2+8*x+1) / (1-x)^13. - Colin Barker, Jul 27 2013
a(n) = 14*(C(n+6,7)^2-C(n+6,6)*C(n+6,8))/((n+6)*(n+1)). - Gary Detlefs, Jan 06 2014
MAPLE
b:=binomial; t73:= proc(a, k) ((2*k+a)*(k+a)/(a^2)) * b(k+a-1, k)*b(k+3*a/2-1, k)/(b(k+a/2, k)); end; [seq(t73(6, k), k=0..40)];
MATHEMATICA
Table[(14 (Binomial[n+6, 7]^2 - Binomial[n+6, 6] Binomial[n+6, 8])/((n + 6) (n + 1))), {n, 50}] (* Vincenzo Librandi, Jan 07 2014 *)
PROG
(Magma) [14*(Binomial(n+6, 7)^2-Binomial(n+6, 6)*Binomial(n+6, 8))/((n+6)*(n+1)): n in [1..30]]; // Vincenzo Librandi, Jan 07 2014
CROSSREFS
Sequence in context: A047646 A010937 A022616 * A041846 A120786 A053063
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2007
STATUS
approved