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Order of universal Chevalley group A_n (3).
16

%I #27 Jun 14 2024 22:31:08

%S 1,24,5616,12130560,237783237120,42064805779476480,

%T 67034222101339041669120,961721214905722855895197286400,

%U 124190524600592082795473760093457612800,144339416867688029764487130056208182629053235200

%N Order of universal Chevalley group A_n (3).

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

%H Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018.

%H Robert Steinberg, <a href="http://www.ms.unimelb.edu.au/~ram/Resources/YaleNotes.pdf">Lectures on Chevalley Groups</a>, Dept. of Mathematics, Yale University, 1967, p. 130-131.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F Numbers so far appear to equal A053290(n)/2. - _Ralf Stephan_, Mar 30 2004

%F a(n) = A(3,n) where A(q,n) = q^(n*(n+1)/2) * Product_{k=2..n+1}(q^k-1). - _Sean A. Irvine_, Sep 18 2015

%t f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}];

%t f[3, #] & /@ Range[0, 9] (* _Michael De Vlieger_, Sep 18 2015 *)

%o (Magma) [&*[(3^n - 3^k): k in [0..n-1]]/2: n in [1..10]]; // _Vincenzo Librandi_, Sep 19 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E One more term from _Sean A. Irvine_, Sep 18 2015