# Couting Self dual functions

The Dual of a Boolean function $F(x_1, x_2, ..., x_n)$, written as $F^D$ is the same expression as that of $F$ with $+$ and $.$ swapped. $F$ is said to be self dual if $$F=F^D$$

How can we count total number of self dual function with $n$ Boolean variables.

I know For $n$ variables total $2^n$ minterms or maxterms are possible and any boolean function can be expressed as combination of minterms or maxterms. But what else is required to count all self dual functions of $n$ variable.

Using de Morgan's laws, we get a more useful characterization of self-dual functions: those are functions satisfying $\lnot F(x_1,\ldots,x_n) = F(\lnot x_1,\ldots,\lnot x_n)$. Suppose that you knew the value of a self-dual function on all inputs in which $x_1$ is false. Can you recover the rest of $F$? Can you deduce the number of self-dual functions?