A003791 Order of universal Chevalley group A_n (8).

1, 504, 16482816, 34558531338240, 4638226007491010887680, 39841906041871272087686291128320, 21903309038581548352789123727634573903790080

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

• Index entries for sequences related to groups.

Crossrefs

Cf. A003787, A003788, A003789, A003790, A003792, A052496, A132036.

Programs

Magma

[&*[(8^n - 8^k): k in [0..n-1]]/7: n in [1..8]]; // Vincenzo Librandi, Sep 19 2015

Mathematica

f[m_, n_] := m^(n (n + 1)/2) Product[m^k - 1, {k, 2, n + 1}]; f[8, #] & /@ Range[0, 6] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A052496(n)/7. - Ralf Stephan, Mar 30 2004

a(n) = A(8,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

a(n) ~ c * 8^(n*(n+2)), where c = (8/7) * A132036 = 0.982178279315... . - Amiram Eldar, Jul 07 2025