Certainly! Here is a Python function to generate test cases for the given "Kode Festival" problem statement.

```python
import random

def tcgen():
    N = random.randint(1, 18)
    A = [random.randint(1, 10**9) for _ in range(2**N)]
    
    return N, A

# Example usage:
if __name__ == "__main__":
    N, A = tcgen()
    print(N)
    for a in A:
        print(a)
```

This function `tcgen()` generates a random value for \(N\) within the range [1, 18] and then generates \(2^N\) random integers within the range [1, 10^9] for the array \(A\). The generated values are printed in the format specified by the problem statement.

You can run this script to generate random test cases to use for testing your solution to the problem.