HDU 5673 Robot 卡特兰数

#include <iostream>
#include <cstdio>
#include <string>
#include <vector>
#include <cstring>
#include <iterator>
#include <cmath>
#include <algorithm>
#include <stack>
#include <deque>
#include <map>
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define mem0(a) memset(a,0,sizeof(a))
#define meminf(a) memset(a,-0x3f,sizeof(a))
#define fi(n) for(i=0;i<n;i++)
#define fj(m) for(j=0;j<m;j++)
#define sca(x) scanf("%d",&x)
#define ssca(x) scanf("%s",x)
#define scalld(x) scanf("%I64d",&x)
#define print(x) printf("%d\n", x)
#define printlld(x) printf("%I64d\n",x)
#define de printf("=======\n")
#define yes printf("YES\n")
#define no printf("NO\n")
typedef long long ll;
using namespace std;

const int mod = 1e9+7;
const int maxn = 1e6+100;

ll inv[maxn];
ll h[maxn];
ll c[maxn];

void init() {
    inv[1] = 1;
    for( int i = 2; i < maxn; i++ ) { // 预处理逆元
        inv[i] = (mod - mod / i) * inv[mod%i] % mod;
    }
}

int main() {
    init();
    int t;
    int n;
    h[0] = h[1] = 1;
    for( int i = 2; i < maxn; i++ ) { // 卡特兰数
        h[i] = h[i-1] * (4*i-2)%mod * inv[i+1] % mod;
    }
    sca(t);
    while( t-- ) {
        sca(n);
        ll ans = 1;
        c[0] = 1;
        for( int i = 1; i <= n; i++ ) { // 组合数
            c[i] = c[i-1] * (n-i+1) % mod * inv[i] % mod;
        }
        for( int i = 1; ; i++ ) {
            int k = n - (i<<1);
            if( k < 0 ) break;
            ans = (ans + h[i] * c[k]) % mod;
        }
        printf( "%lld\n", ans );
    }
    return 0;
}