I have a problem as follows:
Is there a simple formula for in the terms of and only?
I did some calculation as follows:
and hence by the Leibnitz rule
Now, iterating the above formula, I get
And repeating the recursion above as long as possible, I deduce
Particularly, we get
I really wonder to know if there is a simpler formula for this or not?
I feel that there must be a relation between this and the Stirling's numbers.
Lady Moo, may be using the notation in your signature it can be shown simpler?