Number of possibilities to arrange n objects between m objects. I have m objects and insert n indistinguishable objects between them. 
For example, with m=4:
n=1: {0,x,1,2,3},{0,1,x,2,3},{0,1,2,x,3} (3 ways)
n=2:{0,x,x,1,2,3},{0,1,x,x,2,3},{0,1,2,x,x,3},{0,x,1,x,2,3},{0,x,1,2,x,3},{0,1,x,2,x,3} (6 ways)
By counting and guessing I got this formula:
$\frac{1}{(m-2)!}\prod _{i=1}^{m-2} (n+i)$
But I don't know how to derive it. Can somebody help me?

First pretend that the $n$ objects are distinct.  You require that one of the $m$ be first and another be last, so there are $m(m-1)$ ways to select the first and last.  There are $(n+m-2)!$ ways to arrange the rest in the middle, but when we say the $n$ are indistinguishable we have to divide by $n!$.  This gives $m(m-1)\frac {(n+m-2)!}{n!}$ arrangements.
