MathNet 2010 — Part 07 Question 102

An ant starts out at $(0,0)$. Each second, if it is currently at the square $(x, y)$, it can move to $(x-1, y-1)$, $(x-1, y+1)$, $(x+1, y-1)$, or $(x+1, y+1)$. In how many ways can it end up at $(2010,2010)$ after $4020$ seconds?