Multilinear polynomials are in a 1-1 correspondence with linear maps into $\mathbb{R}$, specifically
$$\sum_{i_m \in\\{0,1\\}} a_{i_1 \cdots i_n} x^{i_1} \cdots x^{i_n}$$
is isomorphic to a linear map $\mathbb{R}^{2^n} \to \mathbb{R}$, which can be specified with $2^n$ numbers. So you could generate a random linear map by generating $2^n$ random numbers, and map that to a multilinear polynomial.
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**Edit** Here's an example of how to reproducably generate random numbers in Matlab:
>> seed = 147835;
>> rng(seed); % Set initial seed
>> x = rand(5, 1); % Generate random numbers
>> rng(seed); % Reset the seed
>> y = rand(5, 1); % Generate new random numbers
>> disp([x, y])
0.1171 0.1171
0.6895 0.6895
0.8330 0.8330
0.4596 0.4596
0.8468 0.8468
Note that the same random numbers are generated each time.