Is there a closed form of the following sequence:
$u_0 = 2$
$u_{n+1} = s_n^2-s_n, \;s_n = \sum_{k=0}^{n} u_k$
If not, I would like to have an upper bound. By looking at the numbers I guessed that $2^{2^n}$ is one, is this true? Is there a better one?