Number of partitions of $50$

Does someone know the number of partitions of the integer $50$? I mean, in how many ways can I write $50$ as a sum of positive integers? I know that there's a table by Euler, which is useful to know in how many ways you can write $50$ as a sum of $m$ different numbers, but this table stops at $m=11$, so I can't end the calculation and calculate in how many ways in which I can write $50$ as a sum of (any) different numbers. Thank you

It is known --- and it is a difficult and famous result proven by Hardy and Ramanujan --- that the number of partitions of $n$ is approximately (when $n$ is large) given by $p(n) \sim \frac{ e^{ \pi\sqrt{2n/3} } }{4n\sqrt{3} }$. With $n = 50$, this yelds $p(50) \sim 217590$.

Bad news : there is no useful closed form of $p(n)$. But you can also compute it with the well-known recurrence formula

$$p(n) = p(n-1) + p(n-2) - p(n-5) - p(n-7) + p(n-12) - ... $$

where $1,2,5,7,12$ are the (generalized) pentagonal numbers.

For $n=50$ this could be done with the help of a computer.

(edit : well, as Theophile mentioned, there are tables up to $p(250)$ and more. Also, the sign mistake in the Euler recurrence has been corrected. Thanks !)

According to the table at OEISWiki, the partition number of $50$ is $204226$.