On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$

We obtain an asymptotic formula for the number $S_n$ of repetition-free Boolean functions of $n$ variables in the basis $\{\&,\lor,\oplus,\lnot\}$ for $n\to\infty: S_n\sim cn^{-3/2}\alpha^nn!$, where $c\approx0.1998398363\;,\alpha\approx7.549773429\;.$