[SOLVED] The Leibnitz rule for exponential function?

Hi again,

I have a problem as follows:

Let

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? :p