A later version of the paper referenced above now appears on ArXiv https://arxiv.org/abs/1309.1275 edited by TH Koornwinder after Thomas's death. The appendix by Koornwinter attributes the result originally to

S. Mazur and W. Orlicz, Grundlegende Eigenschaften der polynomischen Operationen. Studia Math. 5 (1934) 50–68.

with

J. Bochnak and J. Siciak, Polynomials and multilinear mappings in topological vector spaces. Studia Math. 39 (1971), 59–76.

giving a slightly more general formula. They agree with Bazin's formula above but without the power of 2.

$$M(v_1,...,v_k) = \frac{1}{k!} \sum\limits_{\epsilon_1,...,\epsilon_k=0}^1 (-1) ^{n- \epsilon_1-\cdots-\epsilon_k} M(\epsilon_1 v_1+ \cdots \epsilon_k v_k)^k $$

A later version of the paper referenced above now appears on ArXiv https://arxiv.org/abs/1309.1275 edited by TH Koornwinder after Thomas's death. The appendix by Koornwinter attributes the result originally to

S. Mazur and W. Orlicz, Grundlegende Eigenschaften der polynomischen Operationen. Studia Math. 5 (1934) 50–68.

with

J. Bochnak and J. Siciak, Polynomials and multilinear mappings in topological vector spaces. Studia Math. 39 (1971), 59–76.

giving a slightly more general formula. They agree with Bazin's formula above but with 0 and 1 instead of +1 and -1 (and hence without the power of 2).

$$M(v_1,...,v_k) = \frac{1}{k!} \sum\limits_{\epsilon_1,...,\epsilon_k=0}^1 (-1) ^{n- \epsilon_1-\cdots-\epsilon_k} M(\epsilon_1 v_1+ \cdots \epsilon_k v_k)^k $$