A003831 Order of universal Chevalley group D_n (4).

3, 3600, 987033600, 67010895544320000, 1154606796534757164318720000, 5081732431326820541485324550799360000000, 5722569627753465177061732369386833143098255605760000000, 1649493899207759406688161287839326786813727965837588934265143296000000000

Offset: 1

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. A003830, A003832, A003834, A003835, A003836.

Programs

Maple

a:= n -> 4^(n*(n-1))*(4^n-1)*mul(4^(2*k)-1, k=1..n-1):
seq(a(n), n=1..8);  # Alois P. Heinz, Jun 24 2025

Mathematica

d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[4, n], {n, 1, 8}] (* Amiram Eldar, Jun 24 2025 *)

Formula

a(n) = D(4,n) where D(q,n) is defined in A003830. - Sean A. Irvine, Sep 17 2015

a(n) ~ c * 4^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/4^(2*k)) = 0.933594707399... . - Amiram Eldar, Jul 08 2025