Stirling numbers of the first kind

$
\begin{array}{lllll}
1 &&&&\\
0 & 1 &&&\\
0 & 1 & 1 &&\\
0 & 2 & 3 & 1 &\\
0 & 6 & 11 & 6 & 1
\end{array}
$
A stirling number of the first kind is the number of permutations of {1, 2, ..., n } with k permutation cycles. Take for example the permutations of {1,2,3 }:
123 - (1)(2)(3)
132 - (1)(23)
213 - (12)(3)
231 - (132)
312 - (132)
321 - (13)(2)
each line consists of the same permutation but in different notation. After the - I noted the permutation in cycle notation. So there are 2 3-permutations of 1 cycle, 3 of 2 cycles and 1 of 3 cycles.