Bell numbers

The Bell number^[https://oeis.org/A000110] $B_n$ counts the number of different ways to partition a set that has exactly $n$ elements, or equivalently, the number of Equivalence relation on it.

$1,1,2,5,15,52,203,877,4140,...$

For the number of different equivalence relations with precisely $k$ equivalence classes, see Second kind (Stirling partition number)

Bell numbers computed using recursive formula

n\\ k \end{array}} \right){B_k}},$$