Polynomials which form the Sheffer sequence for
where is the inverse function of , and have generating function
The first few polynomials are
The Stirling polynomials are related to the Stirling numbers of the first kind by
where is a binomial coefficient and is an integer with (Roman 1984, p. 129).
More things to try:
Weisstein, Eric W. "Stirling Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StirlingPolynomial.html