Can you get the following asymptotics?

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Consider $$ e^{N/d}\frac{d}{2N}\sum_{n=0}^{N-1}\left(\frac{d}{N}\right)^nn! $$ I know its asyptotics when $d<e$ but I haven't suceeded for $d\geq e$. Can you do better and work out its big $N$ asymptotics for $d\geq e$?