cp's OEIS Frontend

A003787 Order of universal Chevalley group A_n (3).

%I A003787 #34 Jul 08 2025 07:51:33
%S A003787 1,24,5616,12130560,237783237120,42064805779476480,
%T A003787 67034222101339041669120,961721214905722855895197286400,
%U A003787 124190524600592082795473760093457612800,144339416867688029764487130056208182629053235200
%N A003787 Order of universal Chevalley group A_n (3).
%D A003787 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 A003787 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 A003787 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 A003787 Robert Steinberg, <a href="https://www.math.utah.edu/~ptrapa/math-library/steinberg/steinberg-yale-notes.pdf">Lectures on Chevalley Groups</a>, Dept. of Mathematics, Yale University, 1967, pp. 130-131.
%H A003787 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>.
%F A003787 Numbers so far appear to equal A053290(n)/2. - _Ralf Stephan_, Mar 30 2004
%F A003787 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
%F A003787 a(n) ~ c * 3^(n*(n+2)), where c = (3/2) * A100220 = 0.840189116891... . - _Amiram Eldar_, Jul 07 2025
%t A003787 f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}];
%t A003787 f[3, #] & /@ Range[0, 9] (* _Michael De Vlieger_, Sep 18 2015 *)
%o A003787 (Magma) [&*[(3^n - 3^k): k in [0..n-1]]/2: n in [1..10]]; // _Vincenzo Librandi_, Sep 19 2015
%Y A003787 Cf. A003788, A003789, A003790, A003791, A003792, A053290, A100220.
%K A003787 nonn,easy
%O A003787 0,2
%A A003787 _N. J. A. Sloane_
%E A003787 One more term from _Sean A. Irvine_, Sep 18 2015