A078592 Call two meanders from A005316 with 2n crossings equivalent if they differ by reflections in the X or Y axes. Sequence gives number of inequivalent meanders.

1, 1, 2, 8, 42, 273, 1970, 15368, 126510, 1086546, 9652364, 88172609, 824506191, 7865294687, 76331857094, 751981532942, 7506432993145, 75811326673326, 773682540353704, 7969986193751019, 82798726340037900, 866804540900696571