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In the case of multiple poles, the classical method of partial fraction expansion (PFE), so often used for the computation of the inverse Z-transform of a rational function, leads to cumbersome expressions for the obtained discrete-time sequences. Exploiting the degrees of freedom left in the PFE, it is possible to obtain time sequences of a simple form. It is shown that the problem thus stated is well defined and that its (simpler) solution can be obtained with the same computational effort as with classical PFE. Two surprisingly elegant properties of the coefficients of the polynomials involved are described, one of which leads to a fast recursive construction scheme for their computation.