Pattern avoidance in "flattened" partitions

To atten a set partition (with apologies to Mathematica r ) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing|increasing entries in each block and blocks arranged in increasing order of their rst entries|we count the partitions of [n] whose attening avoids a single 3-letter pattern. Five counting sequences arise: a null sequence, the powers of 2, the Fibonacci numbers, the Catalan numbers, and the binomial transform of the Catalan numbers.