A003830 Order of universal Chevalley group D_n (3).

2, 576, 12130560, 19808719257600, 2579025599882610278400, 27051378802435080953011843891200, 22941271269626791484963824552883153534976000, 1574947942338058195342953134725345263180893951172280320000

Offset

1,1

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

Robert Israel, Table of n, a(n) for n = 1..32

Robert Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967, pp. 130-131.

Index entries for sequences related to groups

Formula

a(n) = D(3,n) where D(q,n) = q^(n*(n-1)) * (q^n-1) * Product_{k=1..n-1}(q^(2*k)-1). - Sean A. Irvine, Sep 17 2015

Maple

f:= n -> 3^(n*(n-1))*(3^n-1)*mul(3^(2*k)-1, k=1..n-1):
map(f, [$1..10]); # Robert Israel, Sep 22 2015

Mathematica

f[m_, n_] := m^(n (n - 1)) (m^n - 1) Product[m^(2 k) - 1, {k, n - 1}];
f[3, #] & /@ Range@ 8 (* Michael De Vlieger, Sep 17 2015 *)

Prog

(PARI) a(n, q=3) = q^(n*(n-1)) * (q^n-1) * prod(k=1, n-1, q^(2*k)-1); \\ Michel Marcus, Sep 17 2015

Crossrefs

Sequence in context: A159529 A195001 A163277 * A134371 A306635 A212840

Adjacent sequences: A003827 A003828 A003829 * A003831 A003832 A003833

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(8) and formula from Sean A. Irvine, Sep 17 2015

Status

approved