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MATHEMATICA
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nn = 12; q = 2; b[p_, i_] := Count[p, i]; s[p_, i_] :=Sum[j b[p, j], {j, 1, i}] + i Sum[b[p, j], {j, i + 1, Total[p]}]; aut[deg_, p_] := Product[Product[q^(s[p, i] deg) - q^((s[p, i] - k) deg), {k, 1, b[p, i]}], {i, 1, Total[p]}]; \[Nu] = Table[1/n Sum[MoebiusMu[n/m] q^m, {m, Divisors[n]}], n, 1, nn}]; l[greatestpart_] := Level[Table[ IntegerPartitions[n, {0, n}, Range[greatestpart]], {n, 0, nn}], {2}]; g[u_, v_, deg_] := Total[Map[v^Total[#] u^(deg Total[#])/aut[deg, #] &, l[nn]]]; Table[Product[q^n - q^i, {i, 0, n - 1}], {n, 0, nn}] CoefficientList[
Series[1 + Sum[\[Nu][[d]]*(g[u, 1, d] - 1), {d, 1, nn}] , {u, 0, nn}], u]
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