A123501 Signature permutation of a Catalan automorphism: apply *A123497 at the root, then recurse into the left subtree of the right hand side subtree of a binary tree.

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 10, 14, 16, 19, 17, 18, 12, 11, 13, 20, 15, 21, 22, 23, 24, 25, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 45, 46, 48, 49, 50, 31, 34, 30, 28, 29, 35, 33, 32, 36, 54, 55, 40, 39, 41, 57, 43, 58, 59, 61, 52, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71