A069766 Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes180 (A069771) or xReflectHandshakes (A069772) acting on the symmetric parenthesizations encoded by A061855.
0, 1, 2, 3, 5, 4, 6, 7, 11, 9, 10, 8, 12, 17, 14, 21, 19, 13, 20, 16, 18, 15, 22, 23, 37, 29, 33, 27, 41, 25, 39, 31, 32, 26, 40, 35, 36, 24, 38, 30, 34, 28, 42, 57, 47, 72, 64, 44, 68, 54, 61, 51, 76, 59, 49, 74, 66, 43, 67, 53, 60, 50, 75, 70, 46, 71, 56, 58, 48, 73, 63, 65
Offset: 0