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Omni-MATH / A function f:A→A is called idempotent if f(f(x))=f(x) for all x∈A. Let I_(n) be the number of idempotent functions from 1,2,…,n to itself. Compute ∑_(n=1)^(∞)(I_(n))/(n!). · Discussion

Discussing A function f:A→A is called idempotent if f(f(x))=f(x) for all x∈A. Let I_(n) be the number of idempotent functions from {1,2,…,n} to itself. Compute ∑_(n=1)^(∞)(I_(n))/(n!). · Omni-MATH

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