How many ways to split n elements in k groups? * The order of the groups does not matter * The size of group must be at least 1 For example, in a more specific question How many ways to split 5 number in 2 groups?, we got the answer 15 from Jared, which is the sum of 5 ways to split in group size 1 and 4, and 10 ways to to split in group size 2 and 3. For more general cases, what is the formula to calculate this?

These numbers are not very well mannered, They are called the Stirling numbers of the second kind.

see $s(5,2)=15$

For more info see twelvefold way