Print all semimagic squares [closed]

I am working on a code to print all semimagic squares [1] of a given size. I am working with the following definition:

1. An $$\n\times n\$$ consists of numbers $$\1,2,\cdots, n^2\$$.
2. All numbers must be distinct.
3. Sum of each row and each column is equal.

According to Ripatti A. (2018) [1]:

$$\n\$$ number of semimagic squares
1 1
2 0
3 9
4 68 688
5 579 043 051 200
6 94 590 660 245 399 996 601 600
$$\\cdots\$$ $$\\cdots\$$

If someone knows of any resources that could help me, please let me know.

References

1. Ripatti A. (2018) On the number of semi-magic squares of order 6. arXiv. 10.48550/arXiv.1807.02983

• Welcome to Code Golf! This site is for competitive programming challenges, not for questions about coding/mathematics. However, you could make this on-topic by making it into a code-golf challenge (given $n$, output the number of $n \times n$ semi-magic squares), although I'm uncertain how much help that would be to you, given the apparent aim of the question Commented Jun 10, 2023 at 19:21
• This is A271103 (which itself has a reference to Artem Ripatti). Commented Jun 12, 2023 at 12:29