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A182610
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Number of conjugacy classes in GL(n,23).
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17
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1, 22, 528, 12144, 279818, 6435792, 148035360, 3404812752, 78310972608, 1801152369478, 41426510921664, 952809751186128, 21914624425304688, 504036361781716368, 11592836324384010432, 266635235460831961152, 6132610415677439376122, 141050039560581098947824
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..250
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FORMULA
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G.f.: Product_{k>=1} (1-x^k)/(1-23*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)*23^(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:
seq (a(n), n=0..20); # Alois P. Heinz, Nov 03 2012
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MATHEMATICA
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b[n_] := Sum[EulerPhi[d]*23^(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, 20}] (* 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, 23)) : n in [1..4]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-23*x^n) );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */
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CROSSREFS
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Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182611, A182612.
Sequence in context: A158629 A253777 A266884 * A320766 A203456 A271266
Adjacent sequences: A182607 A182608 A182609 * A182611 A182612 A182613
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Nov 23 2010
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EXTENSIONS
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More terms from Alois P. Heinz, Nov 03 2012
MAGMA code edited by Vincenzo Librandi, Jan 24 2013
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STATUS
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approved
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