A001308 Order of Chevalley group D_n (2).

1, 36, 20160, 174182400, 23499295948800, 50027557148216524800, 1691555775522928280469504000, 911666827031785075278550369566720000, 7846393898179181843651374899795632943267840000

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

• T. D. Noe, Table of n, a(n) for n = 1..20
• Index entries for sequences related to groups.

Crossrefs

Cf. A003923, A100221.

Programs

Maple

for m from 0 to 25 do N:=2^(m*(m-1))*mul( 4^i-1, i=1..m-1)*(2^m-1); lprint(N); od:

Mathematica

d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[2, n], {n, 1, 9}] (* Amiram Eldar, Jul 07 2025 *)

Formula

a(n) = 2^(n*(n-1)) * (2^n - 1) * Product_{i=1..n-1} (2^(2*i) - 1).

a(n) ~ c * 2^(n*(2*n-1)), where c = A100221. - Amiram Eldar, Jul 07 2025