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A221583 A sum over partitions (q=18), see first comment. 9
1, 17, 323, 5814, 104958, 1889227, 34011900, 612213877, 11019954438, 198359179578, 3570467115834, 64268408079198, 1156831379431973, 20822964829665048, 374813367546080412, 6746640615829343087, 121439531095946141922, 2185911559727028566514 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Set q=18 and f(m)=q^(m-1)*(q-1), then a(n) is the sum over all partitions P of n over all products prod(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)":

q=3: A006952, q=4: A049314, q=5: A049315, q=7: A049316, q=8: A182603,

q=9: A182604, q=11: A182605, q=13: A182606, q=16: A182607, q=17: A182608,

q=19: A182609, q=23: A182610, q=25: A182611, q=27: A182612.

Sequences where q is not a prime power are:

q=6: A221578, q=10: A221579, q=12: A221580,

q=14: A221581, q=15: A221582, q=18: A221583, q=20: A221584.

LINKS

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

MAPLE

with(numtheory):

b:= proc(n) b(n):= add(phi(d)*18^(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]*18^(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)/(1-18*x^n)  );

v=Vec(gf)

CROSSREFS

Sequence in context: A089571 A196455 A217960 * A091464 A015693 A029535

Adjacent sequences:  A221580 A221581 A221582 * A221584 A221585 A221586

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jan 20 2013

STATUS

approved

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Last modified December 2 17:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)