A lesser-known infinite series for 𝑒pic.twitter.com/LTOZqPXUFP
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Of course, in general one has the following. And B_{k} are called Bell numbers (B₀ = 1, B₁ = 1, B₂ = 2, B₃ = 5, B₄ = 15, B₅ = 52, etc). Bell numbers count the number of ways to partition k elements.pic.twitter.com/a7m64WHesx
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Go for it. It also leads to the nice and surprising-at-first-but-not-for-long formula:pic.twitter.com/pyEdRviGCX
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When I was a freshman in undergrad, I found this (my computing these sums by hand) and thought I had discovered a brand new sequence of integers!! I was only 80+ years too late
tried to even write a paper and publish it to the MAA lmao - 3 more replies
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