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A182611
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Number of conjugacy classes in GL(n,25).
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17
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1, 24, 624, 15600, 390600, 9764976, 244140000, 6103499376, 152587874400, 3814696859400, 95367431234400, 2384185780844400, 59604644765235024, 1490116119130470000, 37252902984364860000, 931322574609121110624, 23283064365380605500600, 582076609134515127375600
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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)/(1-25*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)*25^(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..30); # Alois P. Heinz, Nov 03 2012
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MATHEMATICA
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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 *)
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PROG
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(Magma) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 25)) : n in [1..4]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-25*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, A182610, A182612.
Sequence in context: A167870 A358114 A097192 * A331322 A126153 A002553
Adjacent sequences: A182608 A182609 A182610 * A182612 A182613 A182614
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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 23 2013
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STATUS
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approved
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