The provided code can generate the analytic formula for the Many-Body Hugenholtz diagrams up to order 7 of the MBPT series. Higher-order terms beyond 7 in many-body perturbation theory (MBPT) are also available; however, due to the large size of the data (approximately 10 GB for the eighth order), we are unable to upload them to the GitHub repository. These data can be provided upon reasonable request.

How to run the code:

1. Copy all files in the same directory.
2. Open the Mathematica file "Generate the analytic formula as a divided difference of the Hugenholtz diagram contributions.nb".
3. Execute the code by pressing "Shift+Enter".