Problem #24
Tangles
We define the LEVEL of a triangle as in the following image:
Similarly we can define the LEVEL of a hexagram. It's called level n hexagram if it’s joined by 12 triangles, each one is a level n triangle.
Let us define X(n) as the total number of triangles in a level n hexagram. Then X(n) can be written as a polynomial in terms on n.
Let Y be the product of non-zero coefficients of polynomial X(n). Find the factorial of Y. Since answer can be very large, enter the answer modulo 10^9+9