The history of the Vandermonde notation is described, in the context of the Vandermonde determinant, in <A HREF="http://arxiv.org/abs/1204.4716">A case of mathematical eponymy: the Vandermonde determinant</A>, section 2.1. It seems Lebesgue didn't like it because it could have induced a mix-up between indices and exponents, and that may be a reason it did not survive. Leibniz used a similar notation.

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The following quotation from his 1771 paper shows how Vandermonde used this positional notation for coefficients to construct determinants:

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