A formula for higher order derivatives of inverse function The formula for higher order derivatives of compound functions is known as Faà di Bruno's formula. Does there exist a similar formula for higher order derivatives of an inverse function, i.e. $D^k(f^{-1}(x))$?
I would be most interested in a non-recursive formula, if such exists. A combinatorial term seems unavoidable.
Related: The first derivative of the inverse function is very well known, and the second one is also not that difficult to determine.

As requested by the OP, I add a link to a paper containing the formula and the bibliographic data (in Japanese).
