Suppose we start with n companies that eventually merge into one big
company. How many different ways are there for them to merge?
With three companies {a,b,c}, we need to find the number of ways that
the three companies can become two companies, and for every one of
those possibilities, the two remaining companies can be reduced to one
in only 1 way (because we've already solved the case of two
companies). In the case of {a,b,c}, we can have 1 * [{ab,c}, {ac,b},
{bc,a}], or 3.
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