Exponential generating functions have an $n!$ in the denominator.
Does anyone have references to generating functions with an $n^n$ in the denominator?
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There are no known closed-form functions, either special or elementary, whose series expansion has $n^n$ anyhwere in it. – Lucian Jan 02 '15 at 18:56
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1See Sophomore's dream, OEIS A$073009$, and OEIS A$094082$, as well as this question. – Lucian Jan 03 '15 at 06:00