This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064640 #7 Dec 02 2018 02:51:36 %S A064640 0,1,7,23,127,143,415,659,719,5167,5183,5455,5699,5759,16687,16703, %T A064640 26815,28495,36899,36959,38579,40031,40319,368047,368063,368335, %U A064640 368579,368639,379567,379583,389695,391375,399779,399839,401459,402911,403199 %N A064640 Positions of non-crossing fixed-point-free involutions (encoded by A014486) in A055089, sorted to ascending order. %C A064640 These permutations belong to the interpretation (kk) of the exercise 19 in the sixth chapter "Exercises on Catalan and Related Numbers" of Enumerative Combinatorics, Vol. 2, 1999 by R. P. Stanley, Wadsworth, Vol. 1, 1986: Fixed-point-free involutions w of [2n] such that if i < j < k < l and w(i) = k, then w(j) <> l. %C A064640 From this, it follows that when they are subjected to the same automorphism as used in A061417 and A064636, one gets A002995. %H A064640 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a> %e A064640 The first eight such permutations (after the identity) are in positions 1, 7, 23, 127, 143, 415, 659, 719 of A055089: 21, 2143, 4321, 214365, 432165, 216543, 632541, 654321 which written as disjoint cycles are (1 2), (1 2)(3 4), (1 4)(2 3), (1 2)(3 4)(5 6), (1 4)(2 3)(5 6), (1 2)(3 6)(4 5), (1 6)(2 3)(4 5), (1 6)(2 5)(3 4). %p A064640 sort(A064638); or sort(A064639); %Y A064640 For the needed Maple procedures see A064638. Cf. also A064639, A060112. %K A064640 nonn %O A064640 0,3 %A A064640 _Antti Karttunen_, Oct 02 2001