  We introduce the hook length expansion technique and explain how to discover
old and new hook length formulas for partitions and plane trees. The new hook
length formulas for trees obtained by our method can be proved rather easily,
whereas those for partitions are much more difficult and some of them still
remain open conjectures. We also develop a Maple package HookExp for computing
the hook length expansion. The paper can be seen as a collection of hook length
formulas for partitons and plane trees. All examples are illustrated by HookExp
and, for many easy cases, expained by well-known combinatorial arguments.
