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 A221582 A sum over partitions (q=15), see first comment. 8
 1, 14, 224, 3360, 50610, 759136, 11390400, 170855776, 2562887040, 38443305390, 576650336640, 8649755046240, 129746337080864, 1946195056159200, 29192926013193600, 437893890197853824, 6568408355529888210, 98526125332947516960, 1477891880032655307360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Set q=15 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)*15^(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]*15^(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)/(1-15*x^n)  ); v=Vec(gf) CROSSREFS Sequence in context: A225315 A292041 A145269 * A027774 A099272 A273625 Adjacent sequences:  A221579 A221580 A221581 * A221583 A221584 A221585 KEYWORD nonn AUTHOR Joerg Arndt, Jan 20 2013 STATUS approved

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