We encapsulate bell numbers in a gorgeous formula: e^(e^x-1).
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I learned about Bell numbers and their exponential generating function from Miklós Bóna's "A Walk Through Combinatorics", Third Edition, published by World Scientific Publishing Co. Pte. Ltd. Another explanation of Bell numbers can be found in Herbert Wilf's "Generatingfunctionology", Second Edition.
Негізгі бет Exponential Generating Function for Bell Numbers (Proof)
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