Is there a nice expression for $f(x) = (1+x)(1+x^2)(1+x^3)\cdots$

Question

While I was solving a problem, I stumbled upon this function $$f(x) = (1+x)(1+x^2)(1+x^3)\cdots$$ I tried to write out the first few products but I couldn't recognize any meaningful pattern. Is there some well known facts about this special function?

Thank you very much!

Answer 1

This is the generating function for the number of partitions into distinct parts:

http://mathworld.wolfram.com/PartitionFunctionQ.html