Valid Parenthesis String, Recursion with memoization to DP

How can the following recursion + memoization code be converted into a tabulation format dynamic programming solution?

The code is working but I want to improve it.

The challenge I am facing is handling negative indices (count < 0) and shifting them to the positive side.

Problem link: https://leetcode.com/problems/valid-parenthesis-string/description/

public static boolean checkValidStringMem(String s) 
{
    int n = s.length();
    Boolean[][] mem = new Boolean[n][n + 1];
    return checkValidStringMem(s, 0, 0, mem);
}
public static boolean checkValidStringMem(String s, int i, int count, Boolean[][] mem) 
{
    if (count < 0)
        return false;

    if (i == s.length())
        return count == 0;

    if (mem[i][count] != null)
        return mem[i][count];

    if (s.charAt(i) == '(')
        return mem[i][count] = checkValidStringMem(s, i + 1, count + 1, mem);

    else if (s.charAt(i) == ')')
        return mem[i][count] = checkValidStringMem(s, i + 1, count - 1, mem);

    else // '*' can be ')' or '(' or empty character
    {
        return  mem[i][count] = checkValidStringMem(s, i + 1, count + 1, mem) ||
                                checkValidStringMem(s, i + 1, count - 1, mem) ||
                                checkValidStringMem(s, i + 1, count, mem);
    }
}