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A182609
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Number of conjugacy classes in GL(n,19).
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18
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1, 18, 360, 6840, 130302, 2475720, 47045520, 893864520, 16983555840, 322687560618, 6131066120640, 116490256285320, 2213314916460120, 42052983412605480, 799006685733239040, 15181127028931412160, 288441413566677788022, 5480386857766875373560
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1-x^k)/(1-19*x^k). - Alois P. Heinz, Nov 03 2012
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MAPLE
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with(numtheory):
b:= proc(n) b(n):= add(phi(d)*19^(n/d), d=divisors(n))/n-1 end:
a:= proc(n) a(n):= `if`(n=0, 1,
add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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b[n_] := Sum[EulerPhi[d]*19^(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 *)
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PROG
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(Magma) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 19)) : n in [1..4]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-19*x^n) );
v=Vec(gf)
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CROSSREFS
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Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182610, A182611, A182612.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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