%I #28 Sep 13 2023 11:08:22
%S 1,6,2016,33784128,27811094169600,1122211189922928537600,
%T 2218959336124989671614429593600,
%U 214992513152176999576908105619651923148800,1020690003311610463765638355505358381593396977336320000,237443634207909205360438080389756681126654524500073656592021585920000
%N Number of nonsingular n X n matrices over GF(7).
%H Vincenzo Librandi, <a href="/A053293/b053293.txt">Table of n, a(n) for n = 0..30</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) = (7^n - 1)*(7^n - 7)*...*(7^n - 7^(n-1)).
%F a(n) = A109493(n)*A027875(n). - _Bruno Berselli_, Jan 30 2013
%t Table[Product[7^n - 7^k, {k, 0, n-1}], {n, 0, 10}] (* _Vincenzo Librandi_, Jan 28 2013 *)
%o (Magma) [1] cat [&*[(7^n - 7^k): k in [0..n-1]]: n in [1..7]]; // _Bruno Berselli_, Jan 28 2013
%o (PARI) for(n=0,10, print1(prod(k=0,n-1, 7^n - 7^k), ", ")) \\ _G. C. Greubel_, May 31 2018
%Y Column k=7 of A316622.
%Y Cf. A002884, A003790, A027875, A053290-A053292, A109493.
%K nonn,easy
%O 0,2
%A _Stephen G Penrice_, Mar 04 2000
%E More terms from _Vladeta Jovovic_, Mar 16 2000