|
%I #32 Jun 14 2024 22:31:08
%S 2,576,12130560,19808719257600,2579025599882610278400,
%T 27051378802435080953011843891200,
%U 22941271269626791484963824552883153534976000,1574947942338058195342953134725345263180893951172280320000
%N Order of universal Chevalley group D_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 Robert Israel, <a href="/A003830/b003830.txt">Table of n, a(n) for n = 1..32</a>
%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, pp. 130-131.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = D(3,n) where D(q,n) = q^(n*(n-1)) * (q^n-1) * Product_{k=1..n-1}(q^(2*k)-1). - _Sean A. Irvine_, Sep 17 2015
%p f:= n -> 3^(n*(n-1))*(3^n-1)*mul(3^(2*k)-1,k=1..n-1):
%p map(f, [$1..10]); # _Robert Israel_, Sep 22 2015
%t f[m_, n_] := m^(n (n - 1)) (m^n - 1) Product[m^(2 k) - 1, {k, n - 1}];
%t f[3, #] & /@ Range@ 8 (* _Michael De Vlieger_, Sep 17 2015 *)
%o (PARI) a(n,q=3) = q^(n*(n-1)) * (q^n-1) * prod(k=1,n-1,q^(2*k)-1); \\ _Michel Marcus_, Sep 17 2015
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E a(8) and formula from _Sean A. Irvine_, Sep 17 2015
|
