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Gosper's Algorithm and Bell Numbers

Robert Dougherty-Bliss speaks to the Experimental Mathematics Seminar. Abstract: Computers are now very good at evaluating finite sums in closed form. They can do them almost instantly and can often prove that a sum cannot be evaluated in closed form, like the partial sums of k!. Just like in calculus, we can fix summands that don't yield closed forms by multiplying them by a suitable "summation factor." I will show that this idea, applied to sums of falling factorials, produces sequences of polynomials closely related to the Bell numbers.