 Normally ordered density correlation

This correlation counts distinct detection events without the delta-function self-counting term in an un-ordered product of densities. It is nonnegative as the expectation of $A^{†}A$ with $A={\psi }_n\cdots {\psi }_1$. For a single occupied bosonic mode with sharp occupation $N$, the coincident $n$-point value contains the falling factorial $N(N-1)\cdots (N-n+1)$, rather than $N^n$.