  This is a historical introduction to the theory of Stirling numbers of the
second kind S(n,k) from the point of view of analysis. We tell the story of
their birth in the book of James Stirling (1730) and show how they mature in
the works of Johann Grunert (1843). We demonstrate their usefulness in several
differentiation formulas. The reader can also see the connection to Bernoulli
numbers, to Euler polynomials and to power sums.
