Are there any formulas for coefficients of the polynomial $(1+x)(1+2x)\ldots (1+nx)$?
I can see that coefficient in front of $x^i$ should be a sum of all products of $i$-tuples of numbers $\{1,\ldots ,n\}$. But still - are there any "concise" formulas (not recursive) to compute them?
Reference would be fine, if exists.