Understanding Sylvester sums via symmetric Lagrange interpolation

In 1853, Sylvester introduced double sum expressions for two finite sets of indeterminates and subresultants for univariate polynomials, showing the relationship between both notions in several but not all cases. In 2009, D'Andrea, Hong and two of the authors of the present article completed the description to all possible cases of double sums. Here we show how Sylvester double sums can be interpreted in terms of symmetric multivariate Lagrange interpolation, allowing to recover in a natural way the full description obtained in 2009.