Pension file W.15415, Zebedee Symonds, page 12: declaration of April 1818 naming Capt. Seth Oak's company, Col. Letterlow's regiment.
Image · dated Apr 1818 · source: U.S. National Archives (public record), via Fold3.

How it is shown: Complete page as supplied; no crop, no retouch, no search highlight.
Keep in mind: Symonds (aged 66, of Orange) says he belonged to Capt. Seth Oak's company in Col. Letterlow's regiment for one year ending 6 March 1778. A veteran's (or widow's) declaration that names Capt. Seth Oak's/Oaks' company at Winchendon in 1777. The pension file is another man's; Seth has no pension file of his own. Identification of the Capt. Seth Oak(s) of Winchendon with Seth Oak born 1733 is Likely (the 1906 register says he was 'never a commissioned officer'; a Pension Office agent in 1840 wrote he 'probably acted as Capt.'). The year before 'I belonged' is hard to read and 'Letterlow' is the reading here of the regiment's name.