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%I #35 Sep 13 2023 11:12:13
%S 1,4,480,1488000,116064000000,226614960000000000,
%T 11064475422000000000000000,13506266841692625000000000000000000,
%U 412177498341354683437500000000000000000000000
%N Number of nonsingular n X n matrices over GF(5).
%H Vincenzo Librandi, <a href="/A053292/b053292.txt">Table of n, a(n) for n = 0..35</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) = (5^n - 1)*(5^n - 5)*...*(5^n - 5^(n-1)).
%F a(n) = A109345(n)*A027872(n). - _Bruno Berselli_, Jan 30 2013
%t Table[Product[5^n - 5^k, {k,0,n-1}], {n,0,10}] (* _Geoffrey Critzer_, Jan 26 2013 *)
%o (Magma) [1] cat [&*[(5^n - 5^k): k in [0..n-1]]: n in [1..8]]; // _Bruno Berselli_, Jan 28 2013
%o (PARI) for(n=0,10, print1(prod(k=0,n-1, 5^n - 5^k), ", ")) \\ _G. C. Greubel_, May 31 2018
%Y Column k=5 of A316622.
%Y Cf. A002884, A003789, A027872, A053290, A053291, A053293, A109345.
%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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