F (y) = ∑_{n≥0} \frac{y^{n}}{n!}P_{n}(L_{1}, L_{2}, ⋯, L_{n}, ⋯) (1)

∑_{d} mult(d) = B(n)^{2}  (2)

d⊗1+d_{1}⊗(d_{2}∪d_{3})+d_{2}⊗(d_{1}∪d_{3})+d_{3}⊗(d_{1}∪d_{2})+flips of those (3)

B_{F} (n, y) = ∫_{0}^{+∞} x^{n}W_{F} (x, y)dx  (4)

B_{G}(n, y) = ∫_{0}^{+∞} x^{n}W_{G}(x, y)dx  (5)

W_{F G}(x, y) = ∫_{0}^{+∞} W_{F} (x, z)W_{G}(z, y)dz  (6)