A001308 Order of Chevalley group D_n (2).

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

Offset

1,2

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.

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

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 *)

Crossrefs

Cf. A003923, A100221.

Sequence in context: A271337 A203329 A271338 * A067584 A308423 A146521

Adjacent sequences: A001305 A001306 A001307 * A001309 A001310 A001311

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved