This is the famous 1866 silver set muled with the reverse of 1865 without the motto "In God We Trust". It consists of the quarter dollar J536/P600, half dollar J538/P602 and dollar J540/P605.
These pieces de caprice are believed to have been deliberately struck for Robert Coulton Davis sometime in the later 1860s or early 1870s. The quarter and half dollar were offered in the 1890 sale of his collection but not the dollar. The set was later a part of the Granberg (possibly via Dewitt Smith), Col Green, Boyd and Farouk collections where it was broken up and then reunited in the Willis Dupont collection. The set was stolen along with many other rare coins in 1967. The half and the quarter were recovered in December 1999 and the dollar in early 2004. The set was on display at the ANA until, according to the February 20, 2015 article in Coin World by Paul Gilkes, the Dupont family donated the coins to the Smithsonian in November 2014.
A duplicate dollar ex Chapman, Brand (journal id #20657) is also known. There are questions regarding the pedigrees of the 2 dollars was actually the Davis coin or which is the Farouk coin.
Photos courtesy of the ANA and American Numismatic Rarities.