Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

Solution:
When we see string question with sequence or matching, we should think about dp.
Iteration formula: dp[i][j] = dp[i][j-1] + T[i]==S[j] ? dp[i-1][j-1] : 0.
I tried recursion first, but it exceeded time limited, since it has many duplicate calculations.

DP formula is not clear!!! draw a table!!!

public class Solution {
    public int numDistinct(String S, String T) {
        int[][] dp = new int[T.length()+1][S.length()+1];
        dp[0][0] = 1;
        for(int i = 1; i <= T.length(); i++) dp[i][0] = 0;  // empty S can't contain any T
        for(int j = 1; j <= S.length(); j++) dp[0][j] = 1;  // delete all chars in S
        for(int i = 1; i <= T.length(); i++){
            for(int j = 1; j <= S.length(); j++){
                dp[i][j] = dp[i][j-1];
                if(T.charAt(i-1) == S.charAt(j-1)) dp[i][j] += dp[i-1][j-1];
            }
        }
        return dp[T.length()][S.length()];
    }
}