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Welcome to Mathos channel! Recently, on Twitter, there were some auto-generated binomial coefficients formulas. Let's delve into why these formulas work with a complete solution video. It's all about undergraduate mathematics. Consider the sum denoted as s sub n from k=0 to n of (-1)^k * n choose k squared. This sum represents the coefficient of x^n in the expansion of p sub n equals 1-x^n * 1+x^n. The coefficient simplifies to the sum of (-1)^k * n choose k * n choose n-k. Binomial coefficients symmetry is key here.