\(\text{S}\)¶
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 200 shows the basic use of the \(\text{S}\) function.