若一个问题的结论是通过推线性递推式来解，考虑到实际的情况，可以用BM算法的模板，先输入项数再依次输入项，项越多越准确

#include <bits/stdc++.h>

using namespace std;


#define rep(i,a,b) for(int i=int(a);i<int(b);++i)

#define mem(a,p) memset(a,p,sizeof(a))

#define MAXN 1005

struct BM
{
    int n{};

    vector<double> ps[MAXN];
    int pn{},fail[MAXN]{};
    double delta[MAXN]{};

    void Solve(const double *x,int n)
    {
        pn=0;
        mem(fail,0);
        mem(delta,0);
        ps[0].clear();
        rep(i,1,n+1)
        {
            double dt=-x[i];
            rep(j,0,ps[pn].size())
                dt+=x[i-j-1]*ps[pn][j];
            delta[i]=dt;
            if(fabs(dt)<=1e-8)continue;
            fail[pn]=i;
            if(!pn)
            {
                ps[++pn].resize(1);
                continue;
            }
            vector<double> &ls=ps[pn-1];
            double k=-dt/delta[fail[pn-1]];
            vector<double> cur;
            cur.resize(i-fail[pn-1]-1);
            cur.push_back(-k);
            rep(j,0,ls.size())cur.push_back(ls[j]*k);
            if(cur.size()<ps[pn].size())cur.resize(ps[pn].size());
            rep(j,0,ps[pn].size())cur[j]+=ps[pn][j];
            ps[++pn]=cur;
        }
    }

    void print()
    {
        cout<<setiosflags(ios::fixed)<<setprecision(10);
        for(int i = 0;i<ps[pn].size();++i)
        {
            cout<<ps[pn][i]<<" ";
        }
        cout<<endl;
    }
}B;

double x[MAXN];

int main()
{
    int n;
    while(cin>>n)
    {
        for(int i = 1;i<=n;++i)
        {
            cin>>x[i];
        }
        B.Solve(x,n);
        B.print();
    }
}