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Revision History for A221578
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COMMENTS
Set q=6 and f(m)=q^(m-1)*(q-1), then a(n) is the sum over all partitions P of n over all products prod(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].
Sequences where q is not a prime power are:
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MAPLE
with (numtheory):
add (add (d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
seq (a(n), n=0..30); # Alois P. Heinz, Jan 24 2013
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MATHEMATICA
b[n_] := Sum[EulerPhi[d]*6^(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 *)
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editing
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