> 
> Let $a\_n$ be a number of ordered partitions of the set $\left\{1,\ldots,n\right\}$, which means that order of elements in block is not relevant, but order of blocks does matter. (so $a\_n = \sum\_k\left\{n\atop k\right\}k!$, if I'm not mistaken). Prove recurrence relation:
>  $$a\_0=1; \ a\_n=\sum\_{i=0}^{n-1}{n\choose i} a\_i$$
> 
> 
> 

I don't know if I'm tired or it is just difficult. I tried with combinatorial interpretation but nothing came to my mind, so I tried with formula $a\_n = \sum\_k\left\{n\atop k\right\}k!$ but his also led me to nowhere. Can anybody help?