%I #5 Mar 31 2012 13:21:14
%S 0,1,3,2,7,8,4,5,6,17,18,20,21,22,10,9,11,12,13,14,15,16,19,45,46,48,
%T 49,50,54,55,57,58,59,61,62,63,64,26,27,23,24,25,29,28,30,31,32,33,34,
%U 35,36,38,37,39,40,41,42,43,44,47,51,52,53,56,60,129,130,132,133,134
%N Signature permutation of a Catalan automorphism: inverse of *A130369.
%H A. Karttunen, <a href="/A130370/b130370.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 (*A130370! s) (cond ((not (pair? s))) ((not (pair? (car s))) (*A069770! s)) (else (*A130370! (cdr s)) (*A074680! s))) s)
%Y Inverse: A130369. a(n) = A130371(A074686(n)) = A074686(A130375(n)). The number of cycles, number of fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130377, LEFT(A019590), A130378 and A130379.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 05 2007