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Problem #24

Tangles

We define the LEVEL of a triangle as in the following image:

Triangles

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.

Hexagons

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

Contributed by Sandeep Pathry

Solved by 42 users

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