The conjectural formula for the degree of difficulty

Let $p$ be a polynomial of the special form given by the source's equation, and let $\mathrm{DD}(n)$ denote the associated number of degree of difficulty. Let $A(n-1,1)$ be the quantity defined in the source.

Conjectural formula. The number of degree of difficulty is

$$\mathrm{DD}(n)=A(n-1,1).$$

This is proposed on the basis of an algorithmic implementation; the provided text gives no proof or resolution of the conjecture.