In light of my previous question, I am interested in the following scenario: Let $\tilde Y$ be the blow-up of $Y=\mathbb{P}^n$ along a linear subvariety $X\subseteq Y$ of codimension $d$, i.e. $X\cong\mathbb{P}^{n-d}$. Let $E$ denote the exceptional divisor. Let $H$ be a hyperplane in $Y$ and denote by $P$ the strict transform. I am now interested in the degrees of $P^a E^b$ for $a+b=n$. The only thing related I could find was this post, but I am in a more general setting.

**PS:** I am working over $\mathbb{C}$, so you may assume that, or just any algebraically closed field, or less of course.