A182604 Number of conjugacy classes in GL(n,9).

1, 8, 80, 720, 6552, 58960, 531360, 4782160, 43045920, 387413208, 3486777120, 31380993360, 282429470960, 2541865231440, 22876791858720, 205891126722080, 1853020183479912, 16677181651254480, 150094635248646000, 1350851717237225040, 12157665458621220720

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

G.f.: Product_{k>=1} (1-x^k)/(1-9*x^k). - Alois P. Heinz, Nov 03 2012

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*9^(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

Mathematica

b[n_] := Sum[EulerPhi[d]*9^(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 *)

Prog

(Magma) /* The program does not work for n>6: */ [1] cat [NumberOfClasses(GL(n, 9)): n in [1..6]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-9*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182605, A182606, A182607, A182608, A182609, A182610, A182611, A182612.

Sequence in context: A166157 A145729 A280121 * A320074 A290874 A024101

Adjacent sequences: A182601 A182602 A182603 * A182605 A182606 A182607

Keyword

nonn

Author

Klaus Brockhaus, Nov 23 2010

Extensions

More terms from Alois P. Heinz, Nov 03 2012

MAGMA code edited by Vincenzo Librandi, Jan 24 2013

Status

approved