A003790 - OEIS

%I #27 Jul 08 2025 07:50:38

%S 1,336,5630688,4635182361600,187035198320488089600,

%T 369826556020831611935738265600,

%U 35832085525362833262818017603275320524800,170115000551935077294273059250893063598899496222720000

%N Order of universal Chevalley group A_n (7).

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

%F Numbers so far appear to equal A053293(n)/6. - _Ralf Stephan_, Mar 30 2004

%F a(n) = A(7,n) where A(q,n) is defined in A003787. - _Sean A. Irvine_, Sep 18 2015

%F a(n) ~ c * 7^(n*(n+2)), where c = (7/6) * A100220 = 0.840189116891... . - _Amiram Eldar_, Jul 07 2025

%t f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[7, #] & /@ Range[0, 7] (* _Michael De Vlieger_, Sep 18 2015 *)

%o (Magma) [&*[(7^n - 7^k): k in [0..n-1]]/6: n in [1..10]]; // _Vincenzo Librandi_, Sep 19 2015

%Y Cf. A003787, A003788, A003789, A003791, A003792,A053293, A100220.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E a(7) from _Sean A. Irvine_, Sep 18 2015