Here's a question that arose when I was trying to solve a probability problem in my textbook. I'm trying to calculate the sum:
$$\binom{n}{0}\binom{n + 1}{0} + \binom{n}{1}\binom{n + 1}{1} + \binom{n}{2}\binom{n + 1}{2} + \ldots + \binom{n}{n - 1}\binom{n + 1}{n - 1} + \binom{n}{n}\binom{n + 1}{n}$$
But I'm not sure how to get started with evaluating this. Could anyone help? Any hints would be well-appreciated.