A182608 Number of conjugacy classes in GL(n,17).

1, 16, 288, 4896, 83504, 1419552, 24137280, 410333472, 6975752256, 118587788080, 2015993812032, 34271894799648, 582622235726688, 9904578007265568, 168377826533765184, 2862423051073925184, 48661191875230982480, 827240261878925204256, 14063084452060314850656

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)/(1-17*x^k). - Alois P. Heinz, Nov 03 2012

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*17^(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]*17^(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>4: */ [1] cat [NumberOfClasses(GL(n, 17)) : n in [1..4]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-17*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182609, A182610, A182611, A182612.

Sequence in context: A299939 A218517 A230347 * A320763 A225194 A027776

Adjacent sequences: A182605 A182606 A182607 * A182609 A182610 A182611

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