∀ (σ : Type u_1) (R : Type u_2) [inst : CommRing R] [inst_1 : Fintype σ] [inst_2 : DecidableEq σ] (k : ℕ),
  ↑k * MvPolynomial.esymm σ R k =
    (-1) ^ k *
      ∑ t ∈ MvPolynomial.NewtonIdentities.pairs✝ σ k with t.1.card = k, MvPolynomial.NewtonIdentities.weight✝ σ R k t