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1 ;
1 ;
1 1;
1 1 1;
1 2 1 1;
1 2 1 1 1 1;
1 3 2 2 1 2;
1 3 2 2 1 3 1 0 0 1 0 1;
...
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b[n_, i_] := b[n, i] = If[n == 0 || i == 1, x, b[n, i-1] + Function[{p}, Sum[ Coefficient[p, x, t]*x^LCM[t, i], {t, 1, Exponent[p, x]}]][Sum[b[n-i*j, i-1], {j, 1, n/i}]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Jun 22 2015, after Alois P. Heinz *)
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