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FORMULA
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a(n) = sum {1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n, 1*u_1+2*u_2+...=n, 1*v_1+2*v_2+...=n} (fix A[s_1, s_2, ...;t_1, t_2, ...;u_1, u_2, ...;v_1, v_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...*1^u_1*u_1!*2^u_2*u_2!*...*1^v_1*v_1!*2^v_2*v_2!*...)) where fix A[...] = prod {i, j, k>=1} ( (sum {d|lcm(i, j, k)} (d*v_d))^(s_i*t_j*u_k*lcm(i, j, k)/(i*j*k)))
a(n) asymptotic to n^(n^3)/(n!^4)
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