∀ {R : Type u_1} {σ : Type u_2} [inst : CommSemiring R] (a : σ →₀ R) (s : σ →₀ ℕ) (n : ℕ),
  MvPolynomial.coeff s ((Finsupp.linearCombination R MvPolynomial.X) a ^ n) =
    if (s.sum fun x m => m) = n then ↑s.multinomial * s.prod fun r m => a r ^ m else 0