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a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.
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%I #11 Jun 14 2024 22:31:09

%S 1,1,12,2880,11612160,758041804800,794088208701849600,

%T 13319336815141167562752000,3575164027575627746190393606144000,

%U 15354978274323252140217954794120612413440000,1055182047088717407398960909148529544369642384916480000,1160183823755957350394353874696058298158177597536388268425216000000

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

%C Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).

%D 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 Vincenzo Librandi, <a href="/A028666/b028666.txt">Table of n, a(n) for n = 0..40</a>

%F a(n) = p^n Product (p^n - p^k) for k=0 to n-1

%p f:=proc(n,eps) local m,d;

%p if n mod 2 = 0 then m:=n/2; d:=gcd(4,2^m-eps);

%p 2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;

%p else m:=(n-1)/2;

%p 2^(m^2)*mul( 4^i-1, i=1..m);

%p fi; end;

%p [seq(f(n,+1),n=0..20)]

%t FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]

%Y Bisections give A144546 and A144547.

%K nonn

%O 0,3

%A _Olivier GĂ©rard_

%E Entry revised by _N. J. A. Sloane_, Dec 30 2008