Exponential Transform

The exponential transform is the transformation of a sequence , , ... into a sequence , , ... according to the equation

The inverse ("logarithmic") transform is then given by

The exponential transform relates the number  of labeled connected graphs on  nodes satisfying some property with the corresponding total number  (not necessarily connected) of labeled graphs on  nodes. In this application, the transform is called Riddell's formula for labeled graphs.

REFERENCES:

Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, pp. 19-20, 1995.