  In this note we prove that $\frac{1}{n!} \sum_{\pi} (\sum_{i=1}^n |x_i
a_{i,\pi(i)} |^2)^{1/2}$ is equivalent to a Musielak-Orlicz norm
$\norm{x}_{\sum M_i}$. We also obtain the inverse result, i.e., given the
Orlicz functions, we provide a formula for the choice of the matrix that
generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain
the embedding of 2-concave Musielak-Orlicz spaces into L_1.
