A182605 Number of conjugacy classes in GL(n,11).

1, 10, 120, 1320, 14630, 160920, 1771440, 19485720, 214357440, 2357931730, 25937408640, 285311493720, 3138428201160, 34522710196920, 379749831637440, 4177248147997440, 45949729842155150, 505447028263532520, 5559917313256631160, 61159090445821012920

Offset: 0

Author

Klaus Brockhaus, Nov 23 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182606, A182607, A182608, A182609, A182610, A182611, A182612.

Programs

Magma

N := 300;  R := PowerSeriesRing(Integers(), N);
Eltseq( &*[ (1-x^k)/(1-11*x^k) : k in [1..N] ] ); // Volker Gebhardt, Dec 07 2020

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*11^(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]*11^(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 *)

PARI

N=66; x='x+O('x^N);
gf=prod(n=1,N, (1-x^n)/(1-11*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Formula

G.f.: Product_{k>=1} (1-x^k)/(1-11*x^k). - Alois P. Heinz, Nov 03 2012

Extensions

More terms from Alois P. Heinz, Nov 03 2012