luogu CF932E Team Work |斯特林数

Posted 2021-03-16 naruto-mzx

一句话： 求 (sum^{n}_{i=1}{C(n,i)*i^k})

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题解

#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define ll long long
const int mod=1e9+7,_=5e3+10;
inline int read(){
    int x=0,f=1;
    char c=getchar();
    while(c<'0'||c>'9') f=(c=='-')?-1:1,c=getchar();
    while(c>='0'&&c<='9') x=x*10+c-48,c=getchar();
    return f*x;
}
ll s[_][_];
int n,k;
inline void init(){
    n=read(),k=read();
    s[0][0]=1;
    for(int i=1;i<=k;i++)
    for(int j=1;j<=i;j++)
        s[i][j]=(s[i-1][j-1]+j*s[i-1][j])%mod;
}
inline ll ksm(int b){
    ll ans=1,a=2;
    while(b){if(b&1)ans=ans*a%mod;a=a*a%mod; b>>=1;}
    return ans;
}
signed main(){
    init();
    ll p=ksm(n),ans=0,js=1,inv=500000004;
    for(int i=0;i<=k;i++){
        ans=(s[k][i]*p%mod*js+ans)%mod;
        p=(p*inv)%mod;
        js=js*(n-i)%mod;
    }
    printf("%lld
",ans);
}