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Can someone tell me or just give a hint on how to show that:

[tex]\sum_n \frac{n^2 a^n}{n!}=a(1+a)e^a[/tex]

when n goes to infinity? I know how to show that:

[tex]\sum_n \frac{n a^n}{n!}=a e^a[/tex]

by using the facts that n/n! = 1/(n-1)! and a^n = a a^(n-1). But how can I prove the other one?

Thanks!

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# A simple proof

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