Sure, I can help you create a test case generator for the "What Goes Up Must Come Down" problem statement. Here is the Python code for generating test cases:

```python
import random

def tcgen():
    # Generate a random n within the given constraints
    n = random.randint(1, 100000)
    
    # Generate n random integers between 1 and 100000
    a = [random.randint(1, 100000) for _ in range(n)]
    
    return n, a

# Example of generating and printing a test case
n, a = tcgen()
print(n)
print(' '.join(map(str, a)))
```

This function `tcgen()` generates a random integer \( n \) within the specified range [1, 100000] and then creates a list \( a \) of size \( n \) with random integers between 1 and 100000. The generated test case is returned as a tuple. The final part prints out the generated test case in the required format.

To create multiple test cases, you can call `tcgen()` multiple times within a loop.

Here are some examples of how you might use this in a script to generate multiple test cases:

```python
for _ in range(5):  # Generate 5 test cases
    n, a = tcgen()
    print(n)
    print(' '.join(map(str, a)))
    print()  # Print a blank line to separate test cases
```

This will print 5 test cases, each separated by a blank line. Feel free to adjust the number of test cases according to your needs.