If you go to Google and type in 513th Airborne Infantry Regiment you will find several good places to look. One of them is https://www.ww2-airborne.us/units/513/513.html
This is the home page for the regiment.
If you have your father's old Service Number you can request a copy of his official personnel file. Go to https://www.archives.gov/veterans/military-service-records and follow the instructions.
Hope this info helps.
Dear Ms. Linfante,
Thank you for posting your request on History Hub!
If you have not done so already, we suggest that you request a copy of your father’s Official Military Personnel File (OMPF). OMPFs and individual medical reports for enlisted men of the U.S. Army who were separated from the service after October 1912 and before 1959 are in the custody of NARA's National Personnel Records Center (NPRC) in St. Louis. In many cases where personnel records were destroyed in the 1973 fire, proof of service can be provided from other records such as morning reports, payrolls, and military orders, and a certificate of military service will be issued. Please complete a GSA Standard Form 180 and mail it to NARA's National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. Veterans and their next of kin also may use eVetRecs to request records. See eVetRecs Help for instructions. For more information see Official Military Personnel Files (OMPF), Archival Records Requests.
We searched the Access to Archival Databases (AAD) and located the World War II Army Enlistment Records database that may include a file for your father. If you locate a file for him, you may use the information in it when requesting a copy of his Official Military Personnel File (OMPF). These enlistment records generally include Army serial numbers, which would be the same service number found on a World War II-era dog tag.
Additionally, Headquarters (HDQ) 1 is part of the unit designation, likely the name/number of the company within the 513th Parachute Infantry Regiment (PIR) that your father served in.
Next, we searched the National Archives Catalog and located the World War II Operations Reports, 1940-1948 in the Records of the Adjutant General's Office, 1917-1985 (Record Group 407) that includes records of the 17th Airborne, 513th Parachute Infantry Regiment during WWII. While these records typically do not include information about individuals, they may provide some context for your father’s service, including information about the unit’s actions in specific campaigns or battles. For more information about these non-digitized records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT2. Also, NPRC will continue servicing requests ONLY associated with medical treatments, burials, homeless veterans seeking admittance to a homeless shelter, and those involving the VA Home Loan program. If your request is urgent, please see Emergency Requests and Deadlines. Please refrain from submitting non-emergency requests such as replacement medals, administrative corrections, or records research until NPRC returns to pre-COVID staffing levels. Please check archives.gov/veterans for updates to the NPRC operating hours and status. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this information is helpful. Best of luck with your family research!