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%I #7 Jan 13 2013 06:14:50
%S 0,1,3,2,7,8,6,4,5,17,20,18,21,22,16,19,14,9,11,15,10,12,13,45,54,48,
%T 57,61,46,55,49,58,62,50,59,63,64,44,53,47,56,60,42,51,37,23,28,39,25,
%U 30,33,43,52,38,24,29,40,26,31,34,41,27,32,35,36,129,157,138,166,180
%N Self-inverse permutation of natural numbers induced by the automorphism RotateHandshakes_et_DeepReverse! acting on the parenthesizations encoded by A014486.
%C This automorphism reflects non-crossing handshakes (the interpretation n of Stanley's exercise 19) over the diagonal that goes through corner at "11 o'clock".
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme program for computing this sequence)
%H R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y Composition of A057501 and A057164, i.e. A069888(n) = A057164(A057501(n)). Cf. also A069888.
%K nonn
%O 0,3
%A Antti Karttunen, Apr 16 2002
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