A9462 | On Sum of Number of Inversions in Permutations

Permutation $p$ of length $n$ is the sequence that consists of $n$ distinct integers, each of them is from $1$ to $n$ .

An inversion of permutation $p_{1},p_{2},...,p_{n}$ is a pair of indexes $(i,j)$ , such that $i<j$ and $p_{i}>p_{j}$ .

Permutation $a$ do not exceed permutation $b$ lexicographically, if either $a=b$ or there exists such number $i$ , for which the following logical condition fulfills:  AND $(a_{i}<b_{i})$ .