Show that, for n > 0, the binomial coefficient is divisible by n + 1 and by 4n − 2.
This is an integer, by virtue of its being a binomial coefficient.
Since n and n + 1 are relatively prime, must be divisible by n + 1.
By the previous result, for n > 1, this is an integer. It is an integer by inspection for n = 1.
Therefore, is divisible by 2(2n − 1) = 4n − 2.
Source: Inspired by Catalan Number