  We propose a new formula to compute Witten--Kontsevich intersection numbers.
It is a closed formula, not involving recursion neither solving equations. It
only involves sums over partitions of products of factorials, double factorials
and Kostka numbers (numbers of semi-standard tableau of given shape and weight)
with bounded weights. As an application, we prove a conjecture of [ELO21]
stating that the generating polynomials of the intersection numbers expressed
in the basis of elementary symmetric polynomials have an unexpected vanishing
of their coefficients.
