Two families: S(n,k) (second kind) counts partitions of {1..n} into k non-empty blocks; s(n,k) (first kind, signed) is the coefficient of x^k in x(x-1)…(x-n+1).
Two families: S(n,k) (second kind) counts partitions of {1..n} into k non-empty blocks; s(n,k) (first kind, signed) is the coefficient of x^k in x(x-1)…(x-n+1).