  Since every even power of the Vandermonde determinant is a symmetric
polynomial, we want to understand its decomposition in terms of the basis of
Schur functions. We investigate several combinatorial properties of the
coefficients in the decomposition. In particular, we give recursive formulas
for the coefficient of the Schur function $s_{\m}$ in the decomposition of an
even power of the Vandermonde determinant in $n + 1$ variables in terms of the
coefficient of the Schur function $s_{\l}$ in the decomposition of the same
even power of the Vandermonde determinant in $n$ variables if the Young diagram
of $\m$ is obtained from the Young diagram of $\l$ by adding a tetris type
shape to the top or to the left. An extended abstract containing the statement
of the results presented here appeared in the Proceedings of FPSAC11
