A182609 Number of conjugacy classes in GL(n,19).

1, 18, 360, 6840, 130302, 2475720, 47045520, 893864520, 16983555840, 322687560618, 6131066120640, 116490256285320, 2213314916460120, 42052983412605480, 799006685733239040, 15181127028931412160, 288441413566677788022, 5480386857766875373560

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)/(1-19*x^k). - Alois P. Heinz, Nov 03 2012

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*19^(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]*19^(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, 19)) : n in [1..4]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-19*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182610, A182611, A182612.

Sequence in context: A127585 A230348 A366684 * A320764 A086502 A259459

Adjacent sequences: A182606 A182607 A182608 * A182610 A182611 A182612

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