This combinatorial interpretation provides a recursive formula for
the generating function of the multidegree. We further show that
the total degree of the embedding (thought of as the
projectivization of its cone in
**A**^{2} x **A**^{3} x ... x
**A**^{n-2}) is equal to (2(*n*-3)-1)!!=(2*n*-7)(2*n*-9)...(5)(3)(1). As a consequence, we also obtain a new
combinatorial interpretation for the odd double factorial.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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