A182610 Number of conjugacy classes in GL(n,23).

1, 22, 528, 12144, 279818, 6435792, 148035360, 3404812752, 78310972608, 1801152369478, 41426510921664, 952809751186128, 21914624425304688, 504036361781716368, 11592836324384010432, 266635235460831961152, 6132610415677439376122, 141050039560581098947824

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Formula

G.f.: Product_{k>=1} (1-x^k)/(1-23*x^k). - Alois P. Heinz, Nov 03 2012

Maple

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

Mathematica

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 *)

Prog

(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 */

Crossrefs

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

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