The second kind of Stirling number（连载）

又要开新坑了，这可是个庞大工程。不定期更新！！！
Definition: Stirling number of the second kind is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by $S(n,k)$
$S(n,k)=S(n-1,k-1)+kS(n-1,k) \qquad n\ge k\geq 1$
$S(0,0)=1\quad S(n,0)=S(0,k)=0\quad$

Generating functions:

#include <stdio.h>
#include <algorithm>
using namespace std;
const int prime = 1000000007;
int main() {int n, k;scanf_s("%d%d", &n, &k);int *S = new int[n + 2];//Stirling S(n,k)->S(k)//S(n, k) = S(n - 1, k - 1) + k * S(n - 1, k);S[0] = 0; S[1] = 1;//n=1for (int i = 2; i <= n; ++i) {S[i] = 0;int sj_pre = S[0], sj = S[1];for (int j = 1; j <= i; ++j) {S[j] = sj_pre + j*sj;sj_pre = sj;sj = S[j + 1];}}for (int i = 0; i <= n; ++i)printf("%d ", S[i]);system("pause");return 0;
}