Stirling transform

In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ... } given by In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3, ... } of numbers is the sequence { bn : n = 1, 2, 3, ... } given by where { n k } {displaystyle left{{egin{matrix}n\kend{matrix}} ight}} is the Stirling number of the second kind, also denoted S(n,k) (with a capital S), which is the number of partitions of a set of size n into k parts.