  We analyse the recursive formula found for various Ext groups for $\SL_2(k)$,
$k$ a field of characteristic $p$, and derive various generating functions for
these groups. We use this to show that the growth rate for the cohomology of
$\SL_2(k)$ is at least exponential. In particular, $\max \{\dim
\Ext^i_{\SL_2(k)}(k, \Delta(a))\mid a,i \in \N \}$ has (at least) exponential
growth for all $p$. We also show that $\max \{\dim \Ext^i_{\SL_2(k)}(k,
\Delta(a))\mid a\in \N \}$ for a fixed $i$ is bounded.
