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%I #25 Jun 19 2023 12:11:37
%S 1,15,255,4080,65520,1048305,16776960,268431105,4294962960,
%T 68719407120,1099511558160,17592184926480,281474975596815,
%U 4503599609479680,72057594020040960,1152921504320590335,18446744073423298800,295147905174771671280,4722366482865065107440
%N Number of conjugacy classes in GL(n,16).
%H Alois P. Heinz, <a href="/A182607/b182607.txt">Table of n, a(n) for n = 0..250</a>
%F G.f.: Product_{k>=1} (1-x^k)/(1-16*x^k). - _Alois P. Heinz_, Nov 03 2012
%p with(numtheory):
%p b:= proc(n) b(n):= add(phi(d)*16^(n/d), d=divisors(n))/n-1 end:
%p a:= proc(n) a(n):= `if`(n=0, 1,
%p add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 03 2012
%t b[n_] := Sum[EulerPhi[d]*16^(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 (Magma) /* The program does not work for n>6: */ [1] cat [NumberOfClasses(GL(n, 16)) : n in [1..6]];
%o (PARI)
%o N=66; x='x+O('x^N);
%o gf=prod(n=1,N, (1-x^n)/(1-16*x^n) );
%o v=Vec(gf)
%o /* _Joerg Arndt_, Jan 24 2013 */
%Y Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182608, A182609, A182610, A182611, A182612.
%K nonn
%O 0,2
%A _Klaus Brockhaus_, Nov 23 2010
%E More terms from _Alois P. Heinz_, Nov 03 2012
%E MAGMA code edited by _Vincenzo Librandi_, Jan 24 2013
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