Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122202 with the recursion scheme "KROF", or equivalently row n is obtained as KROF(KROF(n-th row of A089840)). See A122202 for the description of KROF. Each row occurs only once in this table. Inverses of these permutations can be found in table A122289.

REFERENCES

A. Karttunen, paper in preparation, draft available by e-mail.