IIRC the American Battle Monuments Commission returns the service numbers as part of their search results. If he's not listed there, The National Gravesite Locator lists gravesites of veterans. See also U.S. National Cemetery Interment Control Forms, 1928-1962, U.S., Headstone Applications for Military Veterans, 1925-1963, and the U.S., Department of Veterans Affairs BIRLS Death File, 1850-2010 which might be pointers to other records.
In July 2015, Ancestry added a new database, U.S., Social Security Applications and Claims Index, 1936-2007. Their section About U.S., Social Security Applications and Claims Index, 1936-2007 does not say so explicitly, but the URLs of search results suggest that this data comes from the Social Security Administrations Numident records.
The Social Security Administration describes the Numident printout as follows:
A Numident is a query display of the information taken from an
individual's application for an original SSN card and subsequent
applications for replacement SSN cards.
Ancestry's database description discusses the limitations of this database.
It is not an index to all deceased individuals who have held Social
Security Numbers. It is not a database of all deceased individuals who
have received Social Security Benefits, or whose families have
received survivor benefits. Also, persons whose deaths were reported
by the states rather than other institutions may not be included. This
database contains basic information about people with Social Security
numbers whose deaths have been reported to the Social Security
Administration or who would be more than 110 years of age if still