What is the family of generating functions for the *rows* of this Stirling-number matrix for whose columns they are $\exp(\exp(x)-1)-1 $?
Remark: I give much background because it might significantly help to find an idea how to generate a solution I'm analyzing properties of a certain infinite matrix $U$, for whose columns we ...
This is related to an ongoing event. It involves generating the following series : http://oeis.org/A008826 The generating Function as given in the above link is : ...
Here given is a sequence from OEIS. The sequence is triangle of coefficients from fractional iteration of e^x - 1. Few terms are: 1, 1, 3, 1, 13, 18, 1, 50, 205, 180, 1, 201, 1865, 4245, 2700, 1, ...
In Blom, Holst, Sandell, "Problems and snapshots from the world of probability", section 9.4, a model of records is discussed: Elements are ordered in a sequence of increasing length according to ...