Ordered Bell number

The Ordered Bell number is a concept in combinatorial mathematics that counts the number of ways to partition a set into a certain number of non-empty ordered subsets. More formally, the \( n \)-th Ordered Bell number, denoted as \( B_n^{o} \), gives the number of ways to partition a set of size \( n \) into \( k \) non-empty subsets, where the order of the subsets matters.