A003789 Order of universal Chevalley group A_n (5).

1, 120, 372000, 29016000000, 56653740000000000, 2766118855500000000000000, 3376566710423156250000000000000000, 103044374585338670859375000000000000000000000

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, A003790, A003791, A003792, A053292, A100222.

Programs

Magma

[&*[(5^n-5^k): k in [0..n-1]]/4: 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[5, #] & /@ Range[0, 7] (* Michael De Vlieger, Sep 18 2015 *)

Formula

Numbers so far appear to equal A053292(n)/4. - Ralf Stephan, Mar 30 2004

a(n) = A(5,n) where A(q,n) is defined in A003787. - Sean A. Irvine, Sep 18 2015

a(n) ~ c * 5^(n*(n+2)), where c = (5/4) * A100222 = 0.950415994839... . - Amiram Eldar, Jul 07 2025