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

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 $$\binom{n}{0}^2+\binom{n}{1}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}.$$