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
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).
Crossrefs
Cf. A107397.
Programs
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Magma
[Binomial(n+6,6)*Binomial(n+8,6)/28: n in [0..50]]; // Vincenzo Librandi, Jan 07 2014
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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)];
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Mathematica
Table[Binomial[n+6,6]*Binomial[n+8,6]/28, {n,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
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