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A003923
Order of universal Chevalley group B_n (2) or symplectic group Sp(2n,2).
6
1, 6, 720, 1451520, 47377612800, 24815256521932800, 208114637736580743168000, 27930968965434591767112450048000, 59980383884075203672726385914533642240000
OFFSET
0,2
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.
B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.
FORMULA
a(n) = B(2,n) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015
MAPLE
for m from 0 to 50 do N:=2^(m^2)*mul( 4^i-1, i=1..m); lprint(N); od:
MATHEMATICA
a[n_] := 2^(n^2)*Times@@(4^Range[n]-1);
Table[a[n], {n, 0, 8}] (* Jean-François Alcover, Aug 18 2022 *)
PROG
(Python)
from math import prod
def A003923(n): return (1 << n**2)*prod((1 << i)-1 for i in range(2, 2*n+1, 2)) # Chai Wah Wu, Jun 20 2022
CROSSREFS
A bisection of A003053.
Cf. A003920.
Sequence in context: A289747 A188960 A100732 * A002204 A052295 A169668
KEYWORD
nonn,easy,nice
EXTENSIONS
Edited by N. J. A. Sloane, Dec 30 2008
STATUS
approved