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FORMULA
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fix F[ n ]=prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j)-(i=j)n(i)))
a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) where fix A[s_1, s_2, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j} (sum {d|i} (d*s_d))^(i*s_i^2-s_i) or {i != j} (sum {d|lcm(i, j)} (d*s_d))^(2*gcd(i, j)*s_i*s_j)
a(n) asymptotic to (n^(n^2-n))/n! = A090588(n)/A000142(n)
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