Pattern avoidance in "flattened" partitions

To flatten 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 first entries-we count the partitions of vertical bar n vertical bar whose flattening 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. (C) 2008 Elsevier B.V. All rights reserved.