A133355 Dimensions of certain Lie algebra (see reference for precise definition).

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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]

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: (1+8*x+15*x^2+8*x^3+x^4) / (1-x)^13. - Colin Barker, Jul 27 2013

a(n) = 14*(C(n+7,7)^2 - C(n+7,6)*C(n+7,8))/((n+2)*(n+7)). - Gary Detlefs, Jan 06 2014

a(n) = (1/28)*A107397(n). - G. C. Greubel, Feb 09 2025

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[Binomial[n+6, 6]*Binomial[n+8, 6]/28, {n, 0, 50}] (* Vincenzo Librandi, Jan 07 2014 *)

Prog

(Magma) [Binomial(n+6, 6)*Binomial(n+8, 6)/28: n in [0..50]]; // Vincenzo Librandi, Jan 07 2014
(SageMath)
def A133355(n): return binomial(n+6, 6)*binomial(n+8, 6)//28
print([A133355(n) for n in range(31)]) # G. C. Greubel, Feb 09 2025

Crossrefs

Cf. A107397.

Sequence in context: A047646 A010937 A022616 * A041846 A120786 A053063

Adjacent sequences: A133352 A133353 A133354 * A133356 A133357 A133358

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 20 2007

Status

approved