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%I #9 Jul 29 2012 11:51:08
%S 0,1,3,2,8,7,6,5,4,22,21,20,19,18,17,16,15,14,13,12,11,10,9,64,63,62,
%T 61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,
%U 38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,196,195,194,193,192
%N Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.
%C In principle this involution is the signature permutation of yet another Catalan automorphism. However, the question remains what is the most "natural" way to create such an automorphism acting e.g. on S-expressions (i.e. rooted plane binary trees), which would produce this sequence as its signature permutation.
%H A. Karttunen, <a href="/A130918/b130918.txt">Table of n, a(n) for n = 0..2055</a>
%H A. Karttunen, <a href="https://oeis.org/wiki/Signature_permutations_of_Catalan_bijections">Signature permutations of Catalan bijections</a>
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%F a(0)=0, a(n) = A014138(A072643(n)-1) - A082853(n).
%o (Scheme:) (define (A130918 n) (if (zero? n) n (- (A014138 (- (A072643 n) 1)) (A082853 n))))
%Y Inverse: A130918. Cf. A054429, A057163. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130380 and A036987.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 11 2007