思路：
树状dp + 组合数学


import java.math.BigInteger;
class Solution {
    BigInteger fact[];
    BigInteger dp[];
    int MOD=1000000007;
    int cntdp[];
    Map<Integer,TreeNode>map=new HashMap<>();
    public int numOfWays(int[] A) {
        fact=new BigInteger[A.length+1];
        dp=new BigInteger[A.length+1];
        cntdp=new int[A.length+1];        
        
        fact[0]=BigInteger.ONE;
        fact[1]=BigInteger.ONE;
        for(int i=2;i<A.length+1;i++){
            fact[i]=fact[i-1].multiply(BigInteger.valueOf(i));
        }
        
        
        TreeNode root=new TreeNode(A[0]);
        for(int i=1;i<A.length;i++){
            build(root,A[i]);
        }
        post(root);
        
        return (int)(dfs(root).mod(BigInteger.valueOf(MOD)).longValue()-1);
    }
    
    
    public BigInteger dfs(TreeNode root){
        if(root==null)return BigInteger.ONE;
        if(dp[root.val]!=null)return dp[root.val];
        
        BigInteger res=BigInteger.ONE;
        int lcnt=0,rcnt=0;
        if(root.left!=null){
            lcnt=cntdp[root.left.val];
        }
        if(root.right!=null){
            rcnt=cntdp[root.right.val];
        }
        
        if(lcnt==0&&rcnt==0)return BigInteger.ONE;//itself
        
        BigInteger left=dfs(root.left);
        BigInteger right=dfs(root.right);
        
        BigInteger a=res.multiply(left).multiply(right).multiply(F(lcnt+rcnt)).divide(F(lcnt)).divide(F(rcnt));
        BigInteger b=a.mod(BigInteger.valueOf(MOD));
        dp[root.val]=b; 
        return b;
    }
    
    
    
    public BigInteger F(int i){
        return fact[i];
    }
    
    class TreeNode{
        int val=0;
        TreeNode left;
        TreeNode right;
        public TreeNode(int val){
            this.val=val;
        }
    }
    
    public void build(TreeNode root,int v){
        if(v>root.val){
            if(root.right==null){
                root.right=new TreeNode(v);
                return;
            }else{
                build(root.right,v);
            }
        }else{
            if(root.left==null){
                root.left=new TreeNode(v);
                return;
            }else{
                build(root.left,v);
            }
        }
    }
    
    public int post(TreeNode root){
        if(root==null)return 0;
        int l=post(root.left);
        int r=post(root.right);
        
        cntdp[root.val]=1+l+r;
        return cntdp[root.val];
    }
}