OFFSET
0,2
COMMENTS
Set q=12 and f(m)=q^(m-1)*(q-1), then a(n) is the sum over all partitions P of n over all products Product_{k=1..L} f(m_k) where L is the number of different parts in the partition P = [p_1^m_1, p_2^m_2, ..., p_L^m_L].
Setting q to a prime power gives the sequence "Number of conjugacy classes in GL(n,q)":
Sequences where q is not a prime power:
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
MAPLE
with(numtheory):
b:= proc(n) b(n):= add(phi(d)*12^(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, Feb 03 2013
MATHEMATICA
b[n_] := Sum[EulerPhi[d]*12^(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
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-12*x^n) );
v=Vec(gf)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 20 2013
STATUS
approved