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%I #5 Mar 31 2012 13:21:13
%S 0,1,3,2,8,6,5,4,7,22,19,15,16,10,13,21,12,11,20,14,18,17,9,64,60,52,
%T 56,43,41,32,38,47,29,55,27,24,46,36,63,53,59,44,35,62,34,33,61,51,58,
%U 57,42,40,31,39,50,30,37,49,48,28,54,26,25,23,45,196,191,178,186,164
%N Signature-permutation of a Catalan automorphism: composition of A069771 and A125976.
%C Like A069771, A069772, A125976 and A126313/A126314, this automorphism keeps symmetric Dyck paths symmetric, but not necessarily same.
%H A. Karttunen, <a href="/A126315/b126315.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>
%Y Inverse: A126316. a(n) = A069771(A125976(n)) = A126290(A069771(n)) = A126313(A057164(n)). The number of cycles, number of fixed points and maximum cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127281, A127282 and A127283. See also the comment at A127280.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007