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A003830 Order of universal Chevalley group D_n (3). 13
2, 576, 12130560, 19808719257600, 2579025599882610278400, 27051378802435080953011843891200, 22941271269626791484963824552883153534976000, 1574947942338058195342953134725345263180893951172280320000 (list; graph; refs; listen; history; text; internal format)
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, 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

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)