Given $n$ equally spaced points on a circle, we define an $n$-star polygon as an $n$-gon having those $n$ points as vertices. Two $n$-star polygons differing by a rotation/reflection are considered different.

For example, there are twelve $5$-star polygons shown below.

For an $n$-star polygon $S$, let $I(S)$ be the number of its self intersection points.
Let $T(n)$ be the sum of $I(S)$ over all $n$-star polygons $S$.
For the example above $T(5)=20$ because in total there are $20$ self intersection points.

Some star polygons may have intersection points made from more than two lines. These are only counted once. For example, $S$, shown below is one of the sixty $6$-star polygons. This one has $I(S)=4$.

You are also given that $T(8)=14640$.

Find ${\displaystyle \sum _{n=3}^{60}T(n)}$. Give your answer modulo $({10}^9+7)$.