A133238 Dimensions of certain Lie algebra (see reference for precise definition).
1, 52, 1053, 12376, 100776, 627912, 3187041, 13748020, 51949755, 175847880, 542393670, 1544927904, 4107092288, 10278624864, 24388573014, 55188666312, 119696471453, 249869263644, 503865726155, 984563860280, 1869304764600, 3456658569000, 6238533257775
Offset: 0
Keywords
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), 143-179. [Th. 7.1, case a=1]
Crossrefs
Programs
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Maple
b:=binomial; t71:= proc(a,k) ((3*a+2*k+5)/(3*a+5)) * b(k+2*a+3,k)*b(k+5*a/2+3,k)*b(k+3*a+4,k)/(b(k+a/2+1,k)*b(k+a+1,k)); end; [seq(t71(1,k),k=0..30)];
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Mathematica
t71[a_, k_] := (3a+2k+5) / (3a+5) Binomial[k+2a+3,k] Binomial[k+5/2a+3,k] Binomial[k+3a+4,k] / (Binomial[k+a/2+1,k] Binomial[k+a+1,k]); Array[t71[1,#]&,30,0] (* Paolo Xausa, Jan 11 2024 *)
Formula
Empirical g.f.: (x^8+36*x^7+341*x^6+1208*x^5+1820*x^4+1208*x^3+341*x^2+36*x+1) / (x-1)^16. - Colin Barker, Jul 27 2013