Polynomials irreducible by Eisenstein's criterion (Q1403315)

Let \(0=d_0<d_1<\cdots<d_{k-1}<d\) be fixed integers, and let \(E(k,N)\) be the number of polynomials \(X^d+\sum_{i=0}^{k-1}a_iX^{d_i}\), with integral coefficients satisfying \(| a_i| \leq N\) for \(i=0,1,\dots,k-1\), which are \(p\)-Eisensteinian with respect to some prime number \(p\). The author shows that \[ \lim_{N\to\infty}{E(k,N)\over (2N+1)^k}=1-\prod_p\left(1-{1\over p^k}+{1\over p^{k+1}}\right). \]