cp's OEIS Frontend

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

%I A003923 #37 Jul 08 2025 07:49:58
%S A003923 1,6,720,1451520,47377612800,24815256521932800,
%T A003923 208114637736580743168000,27930968965434591767112450048000,
%U A003923 59980383884075203672726385914533642240000,2060902435720151186326095525680721766346957783040000,1132992015386677099994486205757869431795095310094129168384000000
%N A003923 Order of universal Chevalley group B_n (2) or symplectic group Sp(2n,2).
%D A003923 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.
%D A003923 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
%H A003923 T. D. Noe, <a href="/A003923/b003923.txt">Table of n, a(n) for n = 0..20</a>
%H A003923 Bernhard Runge, <a href="https://eudml.org/doc/153497">On Siegel modular forms. Part I</a>, J. Reine Angew. Math., 436 (1993), 57-85.
%H A003923 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>.
%F A003923 a(n) = B(2,n) where B(q,n) is defined in A003920. - _Sean A. Irvine_, Sep 22 2015
%F A003923 a(n) ~ c * 2^(n*(2*n+1)), where c = A100221. - _Amiram Eldar_, Jul 07 2025
%p A003923 for m from 0 to 50 do N:=2^(m^2)*mul( 4^i-1, i=1..m); lprint(N); od:
%t A003923 a[n_] := 2^(n^2)*Times@@(4^Range[n]-1);
%t A003923 Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Aug 18 2022 *)
%o A003923 (Python)
%o A003923 from math import prod
%o A003923 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
%Y A003923 A bisection of A003053.
%Y A003923 Cf. A003920, A100221.
%K A003923 nonn,easy,nice
%O A003923 0,2
%A A003923 _N. J. A. Sloane_
%E A003923 Edited by _N. J. A. Sloane_, Dec 30 2008