栈

#include<stdio.h>
int a[19][19]={0};
int chazhao(int a2,int a3)
{
    if(a3==0&&a2!=0)return 1;
    if(a[a2][a3]!=0)return a[a2][a3];
    if(a2==0)return a[a2+1][a3-1]=chazhao(a2+1,a3-1);
    return a[a2][a3]=(chazhao(a2+1,a3-1)+chazhao(a2-1,a3));
}
int main()
{
    int n,m,i,j,k;
    scanf("%d",&n);
    printf("%d",chazhao(0,n));
}

 http://www.rqnoj.cn/Problem_53.html