## Sum of Squares of a Row of Pascal’s Triangle

https://www.youtube.com/watch?v=jAcbcWV9CyE Similar to the question of summing a row of Pascal’s triangle, we can consider summing the squares of the entires of a row of Pascal’s triangle. By a combinatorial argument involving cats and dogs, we show that $$binom{n}{0}^2+binom{n}{1}^2+cdots+binom{n}{n}^2=binom{2n}{n}.$$