  The decomposition of the Laughlin wave function in the Slater orthogonal
basis appears in the discussion on the second-quantized form of the Laughlin
states and is straightforwardly equivalent to the decomposition of the even
powers of the Vandermonde determinants in the Schur basis. Such a computation
is notoriously difficult and the coefficients of the expansion have not yet
been interpreted. In our paper, we give an expression of these coefficients in
terms of hyperdeterminants of sparse tensors. We use this result to construct
an algorithm allowing to compute one coefficient of the development without
computing the others. Thanks to a program in {\tt C}, we performed the
calculation for the square of the Vandermonde up to an alphabet of eleven
lettres.
