A130371 Signature permutation of a Catalan automorphism: apply *A074685 to the last subtree, if the root degree (A057515(n)) is odd.
0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 19, 22, 18, 17, 23, 24, 25, 27, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 55, 54, 47, 57, 58, 59, 51, 52, 53, 61, 62, 56, 63, 48, 49, 60, 64, 50, 46, 45, 65, 66, 67, 68, 69, 70, 71
Offset: 0