Show directly that the number of configurations in the following problem satisfies the Catalan recurrence
- Sequences $(h_0,\dots , h_{2n})$ of $2n + 1$ non-negative integers $h_i$ such that $h_0 = h_{2n} = 0$ and $h_{i±1} = h_i ± 1$.
I am genuinely lost on this question and would like some tips if possible?