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

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, 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.

Links

T. D. Noe, Table of n, a(n) for n = 0..20

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

Adjacent sequences: A003920 A003921 A003922 * A003924 A003925 A003926

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved