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%I #9 Jan 06 2021 11:36:12
%S 3,18,648,77760,41057280,82771476480,683361309818880,
%T 22304913152488243200,2929259634489976002969600,
%U 1534275894314621670931405209600,3219180858829475639028172057057689600
%N Order of the group GU(n,2), the general unitary n X n matrices over the finite field GF(4).
%C Replacing 2 in the definition by a prime power q, the order of the group GU(n,q), the general unitary n X n matrices over the finite field GF(q^2) is (q+1) * q^(n(n-1)/2) * product i=1..(n-1) (q^(i+1) - (-1)^(i+1)).
%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.
%F For n>=2 a(n) = 3 * 2^(n(n-1)/2) * product i=1..(n-1) (2^(i+1) - (-1)^(i+1))
%t Table[3*2^(n*(n-1)/2) * Product[2^(k+1) - (-1)^(k+1), {k, 1, n-1}], {n, 1, 12}]
%t (* or *) Table[I^(n*(n+3)) * 2^((n-1)*n/2) * QPochhammer[-2, -2, n], {n, 1, 12}] (* _Vaclav Kotesovec_, Jan 06 2021 *)
%o (PARI) for(n=2,30,print1( 3*2^(n*(n-1)/2)*prod(i=1,(n-1),(2^(i+1)-(-1)^(i+1))),","))
%K nonn
%O 1,1
%A Sharon Sela (sharonsela(AT)hotmail.com), May 24 2002
%E More terms from _Benoit Cloitre_, Jun 06 2002
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