This was given to me by my elder nephew. I was able to solve it but in the process I learnt a new concept in numbers called partition number. My nephew taught me a method of how to get to the partition number for a number. He claimed it is called the Chinese method.

Here is the puzzle:

In the following expression, once expanded, what is the coefficient of x^{9 ?}

(1+x)(1+x²)(1+x³)(1+x⁴)(1+x⁵)….(1+x¹⁰⁰)