There is an unsaved comment in progress. You will lose your changes if you continue. Are you sure you want to reopen the work item?
There are interesting for a number of applications: combinatoric, enumerative, translating between representations of polynomials in simple powers of x and rising/falling powers of x.
What makes this problem thorny is that I know of no evaluation method except the recursive one, and that's clearly a problem for large arguments.