cp's OEIS Frontend

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

%I A133355 #35 Feb 10 2025 03:43:43
%S A133355 1,21,210,1386,6930,28314,99099,306735,858858,2212210,5309304,
%T A133355 11992344,25697880,52581816,103285710,195635286,358664691,638489775,
%U A133355 1106715610,1872263250,3097744650,5021809650,7989242625,12491007165,19216934100,29124331236,43526473056
%N A133355 Dimensions of certain Lie algebra (see reference for precise definition).
%H A133355 Vincenzo Librandi, <a href="/A133355/b133355.txt">Table of n, a(n) for n = 0..1000</a>
%H A133355 J. M. Landsberg and L. Manivel, <a href="http://arxiv.org/abs/math/0402157">The sextonions and E7 1/2</a>, arXiv:math/0402157 [math.RT], 2004-2005.
%H A133355 J. M. Landsberg and L. Manivel, <a href="https://doi.org/10.1016/j.aim.2005.02.001">The sextonions and E7 1/2</a>, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=6]
%H A133355 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A133355 G.f.: (1+8*x+15*x^2+8*x^3+x^4) / (1-x)^13. - _Colin Barker_, Jul 27 2013
%F A133355 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
%F A133355 a(n) = (1/28)*A107397(n). - _G. C. Greubel_, Feb 09 2025
%p A133355 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)];
%t A133355 Table[Binomial[n+6,6]*Binomial[n+8,6]/28, {n,0,50}] (* _Vincenzo Librandi_, Jan 07 2014 *)
%o A133355 (Magma) [Binomial(n+6,6)*Binomial(n+8,6)/28: n in [0..50]]; // _Vincenzo Librandi_, Jan 07 2014
%o A133355 (SageMath)
%o A133355 def A133355(n): return binomial(n+6,6)*binomial(n+8,6)//28
%o A133355 print([A133355(n) for n in range(31)]) # _G. C. Greubel_, Feb 09 2025
%Y A133355 Cf. A107397.
%K A133355 nonn,easy
%O A133355 0,2
%A A133355 _N. J. A. Sloane_, Oct 20 2007