Question: How to count the stars in the sky with Maple?

This is the continuation of the question . We have a convex polygon with 9 (a natural number n>3)  vertixes  such that every its point, which is not a vertex, does not belong to three diagonals of that polygon. The question is:
how to count  the number of the sets of the polygon partition by its diagonals?
I have in mind a Maple procedure, not the formula. The answer is 154.

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