Sure, here is the test case generator for the provided problem statement:

```python
import random

def generate_test_case():
    # Step 1: Generate a random N within the given constraints
    N = random.randint(1, 2000)
    
    # Step 2: Generate the array A of size 3N with values between 1 and N (inclusive)
    A = [random.randint(1, N) for _ in range(3 * N)]
    
    return N, A

# Function to print the test case in the required format
def print_test_case(N, A):
    print(N)
    print(' '.join(map(str, A)))

# Generate and print a test case
N, A = generate_test_case()
print_test_case(N, A)
```

### Explanation:
1. **Step 1:** We start by generating a random integer \( N \) within the range [1, 2000]. This represents the number of different integers that can be on the cards.
2. **Step 2:** We then create a list \( A \) of size \( 3N \) where each element is a random integer between 1 and \( N \). This simulates the cards.
3. **Function `print_test_case`:** This function formats and prints the test case as required by the problem statement.

To generate and print a test case, you can run the code block above. It will output \( N \) followed by the sequence \( A \) in the required format.