The asymptotics of the number of repetition-free Boolean functions in the basis $B_1$

For the number $S_n$ of repetition-free Boolean functions of $n$ variables in the basis $B_1$, it is proved that, as $n\to\infty$,
$$ S_n\sim cn^{-3/2}\alpha^nn!, $$
where $c$ and $\alpha$ are some constants.