CF932E Team Work（第二类斯特林数）

Posted 2021-01-11 bztminamoto

求$sum_{i=1}^nC_{n}^i*i^k$

 

题解

 1 //minamoto
 2 #include<iostream>
 3 #include<cstdio>
 4 using namespace std;
 5 const int N=5005,P=1e9+7,inv2=500000004;
 6 inline int ksm(int a,int b){
 7     int res=1;
 8     while(b){
 9         if(b&1) res=1ll*res*a%P;
10         a=1ll*a*a%P,b>>=1;
11     }
12     return res;
13 } 
14 int n,k,S[N][N],ans;
15 int main(){
16 //    freopen("testdata.in","r",stdin);
17     scanf("%d%d",&n,&k);S[0][0]=1;
18     for(int i=1;i<=k;++i) for(int j=1;j<=k;++j)
19     S[i][j]=(S[i-1][j-1]+1ll*j*S[i-1][j])%P;
20     for(int j=0,pw=ksm(2,n),nw=1;j<=min(n,k);pw=1ll*pw*inv2%P,nw=1ll*nw*(n-j)%P,++j)
21     ans=(ans+1ll*S[k][j]*nw%P*pw%P)%P;
22     printf("%d
",ans);
23     return 0;
24 }