I know that the Stirling cycle numbers $\left[{n}\atop{k}\right]$ and Stirling subset numbers $\left\{{n}\atop{k}\right\}$ both satisfy recursion relations on both $n$ and $k$:
$\left[{n}\atop{k}\right]=(n-1)\left[{n-1}\atop{k}\right]+\left[{n-1}\atop{k-1}\right]$
$\left\{{n}\atop{k}\right\}=k\left\{{n-1}\atop{k}\right\}+\left\{{n-1}\atop{k-1}\right\}$
and it is a simple matter to write a program for computing them when you have a two dimensional array available to you.
Is it possible to compute these numbers if all you can use is a one dimensional array (not of course counting the approach where a one dimensional array is treated as a two dimensional array with appropriate indexing)?