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A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.

%I A028666 #20 Jul 14 2025 14:30:29
%S A028666 1,12,2880,11612160,758041804800,794088208701849600,
%T A028666 13319336815141167562752000,3575164027575627746190393606144000,
%U A028666 15354978274323252140217954794120612413440000,1055182047088717407398960909148529544369642384916480000,1160183823755957350394353874696058298158177597536388268425216000000
%N A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.
%C A028666 Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).
%D A028666 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. xii (but beware typos!).
%H A028666 Vincenzo Librandi, <a href="/A028666/b028666.txt">Table of n, a(n) for n = 0..39</a>
%F A028666 a(n) = 4^n * Product_{k=0..n-1} (4^n - 4^k).
%F A028666 a(n) ~ c * 4^(n^2+n), where c = A100221. - _Amiram Eldar_, Jul 14 2025
%p A028666 f:=proc(n,eps) local m,d;
%p A028666 if n mod 2 = 0 then m:=n/2; d:=gcd(4,2^m-eps);
%p A028666 2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;
%p A028666 else m:=(n-1)/2;
%p A028666 2^(m^2)*mul( 4^i-1, i=1..m);
%p A028666 fi; end;
%p A028666 [seq(f(n,+1),n=0..20)]
%t A028666 FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]
%t A028666 a[n_] := 4^n * Product[4^n - 4^k, {k, 0, n-1}]; Array[a, 10, 0] (* _Amiram Eldar_, Jul 14 2025 *)
%o A028666 (PARI) a(n) = 4^n * prod(k = 0, n-1, 4^n - 4^k); \\ _Amiram Eldar_, Jul 14 2025
%Y A028666 Bisections give A144546 and A144547.
%Y A028666 Cf. A028668, A028670, A028671, A028672, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028684, A028686.
%Y A028666 Cf. A100221.
%K A028666 nonn
%O A028666 0,2
%A A028666 _Olivier Gérard_
%E A028666 Entry revised by _N. J. A. Sloane_, Dec 30 2008
%E A028666 Duplicate term 1 removed by _Amiram Eldar_, Jul 14 2025