A003923 Order of universal Chevalley group B_n (2) or symplectic group Sp(2n,2).

1, 6, 720, 1451520, 47377612800, 24815256521932800, 208114637736580743168000, 27930968965434591767112450048000, 59980383884075203672726385914533642240000, 2060902435720151186326095525680721766346957783040000, 1132992015386677099994486205757869431795095310094129168384000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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 = 0..20
• Bernhard Runge, On Siegel modular forms. Part I, J. Reine Angew. Math., 436 (1993), 57-85.
• Index entries for sequences related to groups.

Crossrefs

A bisection of A003053.

Cf. A003920, A100221.

Programs

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 *)

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

Formula

a(n) = B(2,n) where B(q,n) is defined in A003920. - Sean A. Irvine, Sep 22 2015

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

Extensions

Edited by N. J. A. Sloane, Dec 30 2008