%I #6 Oct 15 2015 10:55:23
%S 0,1,3,2,6,8,7,5,4,15,14,19,20,22,16,21,18,11,13,17,12,10,9,39,41,40,
%T 38,37,52,51,53,55,54,60,61,62,64,43,42,56,57,63,47,59,48,29,28,50,33,
%U 34,36,44,58,49,30,35,46,32,25,27,45,31,26,24,23,113,112,117,118,120
%N Permutation of natural numbers induced by the Catalan bijection gmA074681! acting on the parenthesizations encoded by A014486/A063171.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (with the complete Scheme source)
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme function implementing this automorphism on list-structures:)
%o (define (gmA074681! s) (cond ((pair? s) (gmrobl! s) (gmA074681! (car s)) (gmA074681! (cdr s)))) s)
%Y Inverse of A074682. a(n) = A057163(A074684(A057163(n))). Cf. A074685, A074687, A074689. Occurs in A073200 as row 5572432.
%K nonn
%O 0,3
%A _Antti Karttunen_, Sep 11 2002