51 Nod 1556计算(默慈金数的应用)

#include<bits/stdc++.h>

#define mod 1000000007

using namespace std;

typedef long long ll;

ll moni[1000005];

ll exgcd(ll a, ll b, ll &x, ll &y)

{

    if (b == 0)

    {

        x = 1;

        y = 0;

        return a;

    }

    ll r = exgcd(b, a % b, x, y);

    ll t = x % mod;

    x = y % mod;

    y = ((t - a / b * y) % mod + mod) % mod;

    return r;

}

ll inv[1000005];

void init()

{

    inv[1] = 1;

    for(int i = 2; i < 1000002; i ++)

        inv[i] = (mod - mod / i) * 1ll * inv[mod % i] % mod;

moni[1]=1;

    moni[2]=2;

    for(int i=3;i<=1000000;i++)

        moni[i]=((((2*i+1)*moni[i-1]%mod+1ll*3*(i-1)*moni[i-2]%mod)%mod)*inv[i+2]%mod)%mod;

}

ll ans[1000005];

int main()

{

    #ifndef ONLINE_JUDGE

        //freopen("in.txt","r",stdin);

    #endif // ONLINE_JUDGE

    init();

    int n;

    cin>>n;

    ans[1]=1;

    ans[2]=2;

    for(int i=3;i<=n;i++)

        ans[i]=(1ll*ans[i-1]*3%mod-moni[i-2]+mod)%mod;

    cout<<ans[n]<<endl;

    return 0;

}