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%I #5 Mar 31 2012 13:21:14
%S 0,1,2,3,4,6,5,7,8,9,10,11,16,19,14,15,12,17,18,13,20,21,22,23,25,24,
%T 26,27,28,29,30,44,47,33,53,56,60,37,38,39,43,52,42,40,31,45,46,32,48,
%U 49,50,51,41,34,54,55,35,57,58,59,36,61,62,63,64,65,66,67,72,75,70,71
%N Signature permutation of a Catalan automorphism: swap the two rightmost subtrees of general trees, if the root degree (A057515(n)) is even.
%C This self-inverse automorphism is obtained as either SPINE(*A129608) or ENIPS(*A129608). See the definitions given in A122203 and A122204.
%H A. Karttunen, <a href="/A130339/b130339.txt">Table of n, a(n) for n = 0..2055</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%o (Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:)
%o (define (*A130339! s) (if (even? (length s)) (*A129608! s)) s)
%Y Cf. a(n) = A057508(A130340(A057508(n))) = A057164(A130340(A057164(n))). Row 3608 of A122285 and A122286. a(n) = A129608(n), if A057515(n) mod 2 = 0, otherwise a(n)=n.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 05 2007