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A182611 Number of conjugacy classes in GL(n,25).

%I A182611 #28 Jun 19 2023 12:13:20
%S A182611 1,24,624,15600,390600,9764976,244140000,6103499376,152587874400,
%T A182611 3814696859400,95367431234400,2384185780844400,59604644765235024,
%U A182611 1490116119130470000,37252902984364860000,931322574609121110624,23283064365380605500600,582076609134515127375600
%N A182611 Number of conjugacy classes in GL(n,25).
%H A182611 Alois P. Heinz, <a href="/A182611/b182611.txt">Table of n, a(n) for n = 0..250</a>
%F A182611 G.f.: Product_{k>=1} (1-x^k)/(1-25*x^k). - _Alois P. Heinz_, Nov 03 2012
%p A182611 with(numtheory):
%p A182611 b:= proc(n) b(n):= add(phi(d)*25^(n/d), d=divisors(n))/n-1 end:
%p A182611 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182611        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182611     end:
%p A182611 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 03 2012
%t A182611 b[n_] := Sum[EulerPhi[d]*25^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 17 2014, after _Alois P. Heinz_ *)
%o A182611 (Magma) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 25)) : n in [1..4]];
%o A182611 (PARI)
%o A182611 N=66; x='x+O('x^N);
%o A182611 gf=prod(n=1,N, (1-x^n)/(1-25*x^n)  );
%o A182611 v=Vec(gf)
%o A182611 /* _Joerg Arndt_, Jan 24 2013 */
%Y A182611 Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182610, A182612.
%K A182611 nonn
%O A182611 0,2
%A A182611 _Klaus Brockhaus_, Nov 23 2010
%E A182611 More terms from _Alois P. Heinz_, Nov 03 2012
%E A182611 MAGMA code edited by _Vincenzo Librandi_, Jan 23 2013