# $$\text{S}$$¶

You can use the $$\text{S}$$ function to calculate Sterling numbers of the second kind.

You can use the \sterling2fn backslash command to insert this function.

The following variants of this function are available:

• $$\text{real } \text{S} \left ( \text{<n>}, \text{<k>} \right )$$

Where $$\text{<n>}$$ and $$\text{<k>}$$ represents the number of elements and number of disjoint cycles respectively.

The function returns the number of permutations calculated by the recurrence relation:

$\text{S} \left ( n, k \right ) = \frac{1}{k!} \sum_{i = 0}{k} \left ( -1 \right ) ^ i \binom{k}{i} \left ( k - i \right ) ^ n$

Figure 197 shows the basic use of the $$\text{S}$$ function.

Figure 197 Example Use Of The S Function