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May 13, 2021 at 17:53 comment added Fedor Petrov @fsI if $r$ is fixed, the asymptotics is obtained by the saddle point method
May 13, 2021 at 11:15 answer added Peter Taylor timeline score: 4
May 13, 2021 at 5:56 comment added fs l Thanks, I tried this method, it remains to bound the coefficient of $x^m$ on $\left(1+x+\cdots+x^{r-1}\right)^m$
May 13, 2021 at 5:14 comment added Pietro Majer To get bounds and asymptotics on the sequence $N(m)$ it is much easier to work with its generating function. Check e.g. Richard Stanley's Enumerative Combinatorics
May 13, 2021 at 4:51 history asked fs l CC BY-SA 4.0