Anybody shell know this very important formula:

where are the Bell's numbers of x-th order and . For integer x one can find them here:

http://www.research.att.com/~njas/sequences/A111672

http://www.research.att.com/~njas/sequences/A144150

http://www.research.att.com/~njas/sequences/A153277

This formula can be easily derived from regular teration, but has a long history dating from 1945 ( J. Ginsburg, Iterated exponentials, Scripta Math. 11 (1945), 340-353.)

It is notable that tetration and Bell's polynomials of n-th order have applications in quantum physics: http://arxiv.org/abs/0812.4047

where are the Bell's numbers of x-th order and . For integer x one can find them here:

http://www.research.att.com/~njas/sequences/A111672

http://www.research.att.com/~njas/sequences/A144150

http://www.research.att.com/~njas/sequences/A153277

This formula can be easily derived from regular teration, but has a long history dating from 1945 ( J. Ginsburg, Iterated exponentials, Scripta Math. 11 (1945), 340-353.)

It is notable that tetration and Bell's polynomials of n-th order have applications in quantum physics: http://arxiv.org/abs/0812.4047