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%I #13 Jul 09 2018 02:46:27
%S 1,30,15500,453375000,95367431640625,1200572419921875000000,
%T 216114100769531250000000000000,
%U 2795257557110966548919677734375000000000,209657627533594448152542114257812500000000000000000,1062251098375118429310154377631647548696491867303848266601562500
%N Number of n X n matrices over GF(5) with characteristic polynomial x^n - 1.
%H I. Reiner, <a href="https://projecteuclid.org/euclid.ijm/1255629830">On the number of matrices with given characteristic polynomial</a>, Illinois J. Math. 5 1961 324-329.
%o (PARI) \\ see Reiner reference.
%o F(u,r)={prod(i=1, r, (1-u^(-i)))}
%o a(n, q=5)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ _Andrew Howroyd_, Jul 08 2018
%Y Cf. A088654, A089035, A089036.
%K nonn
%O 1,2
%A Yuval Dekel (dekelyuval(AT)hotmail.com) and _W. Edwin Clark_, Nov 29 2003
%E Offset corrected and a(8)-a(10) from _Andrew Howroyd_, Jul 08 2018
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