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%I #8 Jan 13 2013 06:14:46
%S 0,1,3,2,7,5,8,4,6,17,12,20,10,15,18,13,21,9,14,22,11,16,19,45,31,54,
%T 26,40,48,34,57,24,38,61,29,43,52,46,32,55,27,41,49,35,58,23,37,62,28,
%U 42,51,50,36,59,25,39,63,30,44,53,64,33,47,56,60,129,87,157,73,115,138
%N Self-inverse permutation of natural numbers induced by the automorphism DeepReverse_et_RotateHandshakes! 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 "1 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 A057164 and A057501, i.e. A069888(n) = A057501(A057164(n)). Cf. also A069889.
%K nonn
%O 0,3
%A Antti Karttunen, Apr 16 2002, suggested by Wouter Meeussen Dec 15 2001.
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