Stirling number of the second kind

Stirling number of the second kind or Stirling partition number counts the number of partitions of the set of objects into nonempty blocks.

It is denoted as or .

For , we have the following recurrence relation

Examples

Ex: Partitions: 1|23, 2|13, 3|12 Thus,

Ex: Partitions

• 1|234, 2|134, 3|124, 4|123
• 12|34, 13|24, 14|23 Therefore,