'Luman of Marlow and Charlestown, N. H., b. 15 May ----' is listed last of the 7 children of Nathan and Luce Huntley, probably because his birth year was unknown.
Note that this article also says that Nathan Huntley sold his property in Lyme and migrated to Marlow (New Hampshire) in 1761.
Luman Huntley 1 male and 1 female aged 60-69 [born 1760-1770] 1 male aged 20-29
↑ While the 1830 census suggests he was born in or after 1760, his birth is recorded in the Lyme Vital records, so he presumably was born before 1761. 15 May 1756 fills a gap in the birth records of his siblings, and seems to be a reasonably well-accepted birth date.