Pascal's Triangle

Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it. The pattern starts with 1 at the top, and each subsequent row begins and ends with 1. The algorithm uses a mathematical formula to calculate each value in the triangle: for each position (i, j), the value is calculated as val = val * (i - j + 1) / j, where val starts as 1 for each row. This formula efficiently computes the binomial coefficients without having to store the entire triangle.