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%I #5 Mar 31 2012 13:21:13
%S 0,1,3,2,6,8,7,5,4,15,20,14,19,21,18,22,16,11,13,17,12,10,9,39,53,41,
%T 55,59,40,54,38,52,57,37,51,56,58,47,60,49,62,64,48,61,43,29,34,42,28,
%U 33,35,50,63,46,32,36,44,30,25,27,45,31,26,24,23,113,155,118,160,173
%N Signature-permutation of a Catalan automorphism: composition of A127291 and A057164.
%C This is otherwise like A127291, but uses A127285 instead of A127287 as a "picker permutation" for the function "tau", which can be found in the entry A127291. A014486->parenthesization is given in A014486. This permutation contains some exceptionally large cycles, see A127297.
%H A. Karttunen, <a href="/A127289/b127289.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 (Scheme:) (define (A127289 n) (tau (A014486->parenthesization (A014486 n)) *A127285!))
%Y Inverse: A127290. a(n) = A127291(A057164(n)) = A057164(A127299(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127296, A127297 and A127298.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 16 2007
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