It was in that combinatorics class where I learned about some of the patterns inside Pascal’s triangle — and the narratives they encapsulated. One of the patterns in Pascal’s triangle is that the sums ...

For example, adding up all the numbers in the first 5 rows of Pascal’s triangle gives us the 5th Mersenne number, 31 (which is 1 less than 2 to the power of 5).

As you’ll recall, this triangle of numbers has a 1 in the top row and 1s along both edges, and each subsequent row is built by adding pairs of numbers from the previous. So the first row is just ...