I want to study the asymptotic behavior of the following recurrence relation:$y_1=1$;$y_{n+1}=y_{n}+(1+\frac{y_n}{n})^{-n}\ \ $ for $n\ge 1$.I made an initial attempt and guessed that $y_{n} \sim Log(n)$.Any referrence or hint about this might be helpful. Any help will be greatly appreciated
Asymptotic of interesting recurrence relation
asymptotics;recurrence relation