A003790 Order of universal Chevalley group A_n (7).

1, 336, 5630688, 4635182361600, 187035198320488089600, 369826556020831611935738265600, 35832085525362833262818017603275320524800, 170115000551935077294273059250893063598899496222720000

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, A003791, A003792,A053293, A100220.

Programs

Magma

[&*[(7^n - 7^k): k in [0..n-1]]/6: n in [1..10]]; // Vincenzo Librandi, Sep 19 2015

Mathematica

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 *)

Formula

Numbers so far appear to equal A053293(n)/6. - Ralf Stephan, Mar 30 2004

a(n) = A(7,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

a(n) ~ c * 7^(n*(n+2)), where c = (7/6) * A100220 = 0.840189116891... . - Amiram Eldar, Jul 07 2025

Extensions

a(7) from Sean A. Irvine, Sep 18 2015