A bijection between certain non-crossing partitions and sequences

AbstractWe 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 {si}1n such that 1⩽si⩽i, and if si=j, then si-r⩽j-r for 1⩽r⩽j-1