Coefficient of  X2020  in (1 + X + X2 + X3)1010 (1 – X)1011 is

The problem can be solved using the Binomial Theorem. Here are the steps:

1. Expand the expression (1 + X + X^2 + X^3)^1010 using the Binomial Theorem. This will give you a series of terms, each of which is a coefficient times X raised to a power. The power of X in each term is the sum of the powers of X in the corresponding terms of the original expression.

2. Similarly, expand the expression (1 – X)^1011 using the Binomial Theorem. This will give you another series of terms, each of which is a coefficient times X raised to a power. The power of X in each term is the sum of the powers of X in the corresponding terms of the original expression.

3. Multiply the two series together. This will give you a new series of terms, each of which is a coefficient times X raised to a power. The power of X in each term is the sum of the powers of X in the corresponding terms of the two original series.

4. Find the term in the new series that has X raised to the power 2020. The coefficient of this term is the answer to the problem.

Note: This is a very complex problem that requires a deep understanding of the Binomial Theorem and a lot of computation. It's not something that can be easily solved by hand. You would typically use a computer algebra system to do the computations.