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Partition polynomials constructed from the face structures of the associahedra (OEIS A133437) and permutahedra (A133314) comprise the antipodes/compositional inverses in a Faa-di-Bruno-type Hopf ...

Three particularly important reps of the exponential formula (cf. MO-Q) are the refined Lah polynomials (OEIS A130561): Exp[o.g.f.] = Exp[formal power series]$\; =\exp[\frac{1}{(1-a.x)}]$, umbrally ...