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Hello and welcome to the mathos channel in english recently I saw on twitter some automatically generated formula about binomial coefficients which looked like this. Pretty nice isnt it ? Then someone asked the right question : yes, but why ? So I decided to produce a short video, providing a complete solution to that question. As youll see, its all about undergraduate mathematics, but i think its well worth the visit. Consider s sub n which denotes the sum for k equals 0 to n of negative 1 to the kth power multiplied by n choose k squared. The key idea is that s sub n can be considered as the coefficient of x^n in the expansion of the following polynomial : p sub n equals 1 minus x to the n multiplied by 1 plus x to the n. Indeed, that coefficient appears at first glance to be the sum for k equals 0 to n of negative 1 to the k multiplied by the product of n choose k by n choose n minus k. But we know that binomial coefficients are symmetric which
