Because painted trillium is an endangered botanical species, its occurrence is rare.
So a double-flowered trillium is native but exotic, old-fashioned but new.
trillium will send you information about itself and tell you when your membership begins.
British Dictionary definitions for trillium
any herbaceous plant of the genus Trillium, of Asia and North America, having a whorl of three leaves at the top of the stem with a single central white, pink, or purple three-petalled flower: family Trilliaceae
C18: from New Latin, modification by Linnaeus of Swedish trilling triplet