Unsigned Stirling number of the first kind

Definition
The unsigned Stirling number of the first kind $$|s(n,k)|$$, also denoted $$S_1(n,k)$$ or $$c(n,k)$$, is defined as the number of elements in the symmetric group of degree $$n$$ whose cycle decomposition has exactly $$k$$ cycles. (Here, each fixed point is treated as a cycle of size one).

The unsigned Stirling numbers play a role in the probability distribution of number of cycles of permutations.

Particular cases
Note that the unsigned Stirling numbers of the first kind for fixed $$n$$ form a unimodal (single-peaked) sequence in $$k$$, i.e., they are first increasing and then decreasing.