Sequence of polynomials
For a different family of polynomials Q
n occasionally called Touchard polynomials, see
Bateman polynomials.
The Touchard polynomials, studied by Jacques Touchard (1939), also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by
where is a Stirling number of the second kind, i.e., the number of partitions of a set of size n into k disjoint non-empty subsets.[1][2][3][4]
The first few Touchard polynomials are