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%I #47 Sep 13 2023 11:10:57
%S 1,2,48,11232,24261120,475566474240,84129611558952960,
%T 134068444202678083338240,1923442429811445711790394572800,
%U 248381049201184165590947520186915225600,288678833735376059528974260112416365258106470400
%N Number of nonsingular n X n matrices over GF(3).
%H Vincenzo Librandi, <a href="/A053290/b053290.txt">Table of n, a(n) for n = 0..45</a>
%H J. Overbey, W. Traves and J. Wojdylo, <a href="http://jeff.over.bz/papers/undergrad/on-the-keyspace-of-the-hill-cipher.pdf">On the Keyspace of the Hill Cipher</a>.
%F a(n) = Product_{k=0..n-1}(3^n-3^k). - corrected by _Michel Marcus_, Sep 18 2015
%F a(n) = A047656(n)*A027871(n). - _Bruno Berselli_, Jan 30 2013
%t Table[Product[3^n - 3^k, {k, 0, n - 1}], {n, 0, 10}] (* _Geoffrey Critzer_, Jan 26 2013; edited by _Vincenzo Librandi_, Jan 28 2013 *)
%o (Magma) [1] cat [&*[(3^n - 3^k): k in [0..n-1]]: n in [1..9]]; // _Bruno Berselli_, Jan 28 2013
%o (PARI) for(n=0,10, print1(prod(k=0,n-1, 3^n - 3^k), ", ")) \\ _G. C. Greubel_, May 31 2018
%Y Column k=3 of A316622.
%Y Cf. A002884, A003787, A027871, A047656, A053291, A053292, A053293.
%K nonn,easy
%O 0,2
%A _Stephen G Penrice_, Mar 04 2000
%E More terms from _Vladeta Jovovic_, Mar 16 2000
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