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Thank Robin Chapman very much for editing.

There is a nice asymptotic expression for partition $q(n,M)$ that denotes the number of partitions of $n$ with $M$ parts all distinct: As $n\to\infty$,

$$q(n,M)\approx \frac{(n-1)!}{M!(M-1)!(n-N)!}\left( frac{(n-1)!}{M!(M-1)!(n-M)!}\left( 1+O\left( \frac{M^{3}}{n} \right) \right)$$

Isn't there no similar asymptotic expression for partition $p(n,m)$?

Thank Robin Chapman very much for editing.

There is a nice asymptotic expression for partition $q(n,M)$ that denotes the number of partitions of n $n$ with M $M$ parts all distinct: As $n\to\infty$,

$$q(n,M)\approx \frac{(n-1)!}{M!(M-1)!(n-N)!}\left( 1+O\left( \frac{M^{3}}{n}frac{M^{3}}{n} \right) \right)$$

Isn't there no similar asymptotic expression for partition $p(n,m)$?

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Thank Robin Chapman very much for editing.

There is a nice asymptotic expression for partition $q(n,M)$ that denotes the number of partitions of n with M parts all distinct:

$q(n,M)\approx \frac{(n-1)!}{M!(M-1)!(n-N)!}\left( 1+O\left( \frac{M^{3}}{n}$

Isn't there no similar asymptotic expression for partition $p(n,m)$?