CodeM 2018 决赛

A 大力推一下式子 n * sigma i from 2 to n+1 ( C(n-1, i-2) * (i-2)! * (2n-i)! / 2^(n+1-i) ) 就没有然后了 

/* ***********************************************
Author        :BPM136
Created Time  :2018/7/27 10:39:22
File Name     :A.cpp
************************************************ */

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<iomanip>
#include<bitset>
#include<queue>
#include<ctime>
#include<set>
#include<map>
#include<vector>
#include<cassert>
#include<functional>
#define pb push_back
#define popb pop_back
#define MID ((l+r)>>1)
#define LSON (k<<1)
#define RSON (k<<1|1)
#define get(a,i) ((a)&(1<<(i-1)))
#define PAU putchar(32)
#define ENT putchar(10)
#define clr(a,b) memset(a,b,sizeof(a))
#define rep(_i,_a,_b) for(int _i=(_a);_i<=(_b);_i++)
#define down(_i,_a,_b) for(int _i=(_a);_i>=(_b);_i--)
#define FOR(_i,_b) for(int _i=1;_i<=(_b);_i++)
#define efo(_i,_a) for(int _i=last[(_a)];_i!=0;_i=e[_i].next)
#define Remax(a,b) if(b>a) a=b;
#define Remin(a,b) if(b<a) a=b;
#define filein(x) freopen(#x".in","r",stdin)
#define fileout(x) freopen(#x".out","w",stdout)
#define file(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout);
#define mkd(x) freopen(#x".in","w",stdout);
#define setlargestack(x) int _SIZE=x<<20;char *_PPP=(char*)malloc(size)+_SIZE;__asm__("movl %0, %%esp
" :: "r"(_PPP));
#define END system("pause")
#define read2(a,b) read(a),read(b)
#define read3(a,b,c) read(a),read(b),read(c)
#define readg(_x1,_y1,_x2,_y2) read(_x1),read(_y1),read(_x2),read(_y2)
using namespace std;

typedef long long ll;
typedef double DB;
typedef long double LD;
typedef unsigned int  UI;
typedef unsigned long long ULL;
typedef vector<int> VI;
typedef set<int> SI;
typedef set<int , greater<int> > SIG;
typedef map<int, int > MII;
typedef map<int, int, greater<int> > MIIG;

namespace fastIO{  
    #define BUF_SIZE 100000  
    #define OUT_SIZE 100000  
    //fread->read  
    bool IOerror=0;  
    inline char nc(){  
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;  
        if (p1==pend){  
            p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin);  
            if (pend==p1){IOerror=1;return -1;}  
            //{printf("IO error!
");system("pause");for (;;);exit(0);}  
        }  
        return *p1++;  
    }  
    inline bool blank(char ch){return ch==32||ch==10||ch==13||ch==9;}  
    inline bool enter(char ch){return ch==10||ch==13;}
    inline void read(int &x){  
        bool sign=0; char ch=nc(); x=0;  
        for (;blank(ch);ch=nc());  
        if (IOerror)return;  
        if (ch==45)sign=1,ch=nc();  
        for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48;  
        if (sign)x=-x;  
    }  
    inline void read(ll &x){  
        bool sign=0; char ch=nc(); x=0;  
        for (;blank(ch);ch=nc());  
        if (IOerror)return;  
        if (ch==45)sign=1,ch=nc();  
        for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48;  
        if (sign)x=-x;  
    }  
    inline void read(double &x){  
        bool sign=0; char ch=nc(); x=0;  
        for (;blank(ch);ch=nc());  
        if (IOerror)return;  
        if (ch==45)sign=1,ch=nc();  
        for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48;  
        if (ch==46){  
            double tmp=1; ch=nc();  
            for (;ch>=48&&ch<=57;ch=nc())tmp/=10.0,x+=tmp*(ch-48);  
        }  
        if (sign)x=-x;  
    }  
    inline void read(char *s){  
        char ch=nc();  
        for (;blank(ch);ch=nc());  
        if (IOerror)return;  
        for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch;  
        *s=0;  
    }  
    inline void read(char *s,bool f) {
        char ch=nc();
        for (;blank(ch);ch=nc());
        if(IOerror)return;
        for(;!enter(ch)&&!IOerror;ch=nc())*s++=ch;
        *s=0;
    }
    inline void read(char &c){  
        for (c=nc();blank(c);c=nc());  
        if (IOerror){c=-1;return;}  
    } 
#undef OUT_SIZE  
#undef BUF_SIZE  
}; using namespace fastIO;

const int N = 2000005;
const ll MOD = 998244353;

ll inv[N];
ll fac[N];
ll fac_inv[N];
ll bit2_inv[N];

ll C(int n,int m) {
    return fac[n]*fac_inv[m]%MOD*fac_inv[n-m]%MOD;
}

int main() {
    inv[0]=fac[0]=1; inv[1]=1;
    rep(i,1,N-1) fac[i]=fac[i-1]*i%MOD;
    rep(i,2,N-1) inv[i]=(MOD-MOD/i)*inv[MOD%i]%MOD;
    fac_inv[0]=1; rep(i,1,N-1) fac_inv[i]=fac_inv[i-1]*inv[i]%MOD;
    bit2_inv[0]=1; rep(i,1,N-1) bit2_inv[i]=bit2_inv[i-1]*inv[2]%MOD;
    ll n;
    cin>>n;
    ll ans=0;
    rep(i,2,n+1) {
        ans+=C(n-1,i-2) * fac[i-2] % MOD
            *fac[2*n-i] % MOD * bit2_inv[n+1-i] % MOD;
        ans%=MOD;
    }
    cout<<ans*n%MOD<<endl;
    return 0;
}