A bijection between certain non-crossing partitions and sequences
  We present a bijection between non-crossing partitions of the set $[2n+1]$ into $n+1$ blocks such that no block contains two consecutive integers, and the set of sequences $\{s_{i}\}_{1}^{n}$ such that $1 \leq s_{i} \leq i$, and if $s_{i}=j$, then $s_{i-r} \leq j-r$ for $1 \leq r \leq j-1$. 
Rekha Natarajan