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 A350645 #16 Jan 09 2022 23:50:53 %S A350645 1,2,8,36,170,824,4060,20232,101664,514140,2613468,13340496,68335644, %T A350645 351087128,1808405600,9335697424,48289295226,250213951992, %U A350645 1298517484804,6748250144600,35114221973600,182924946400680,953931045159000,4979398271047200,26014703727203100 %N A350645 Number of permutations avoiding 132 of length 3n composed of only 3-cycles. %C A350645 Also the number of permutations avoiding 213 of length 3n composed of only 3-cycles. %H A350645 Kassie Archer and Christina Graves, <a href="https://arxiv.org/abs/2104.12664">Pattern-restricted permutations composed of 3-cycles</a>, arXiv:2104.12664 [math.CO], 2021. %F A350645 G.f.: c(x*c(x))/(2-c(x*c(x))) where c(x) is the generating function for Catalan numbers. Notice c(x*c(x)) is given in A127632. %F A350645 G.f.: (1+A(x))/(1-A(x)) where A(x) = (c(x)-1)*c(m(x)-1) where c(x) is the generating function for Catalan numbers and m(x) is the generating function for the Motzkin numbers. %e A350645 For n=2, the eight permutations (in one-line notation and cycle notation) are: %e A350645 [6, 5, 2, 1, 3, 4] (1,6,4)(2,5,3) %e A350645 [6, 4, 2, 3, 1, 5] (1,6,5)(2,4,3) %e A350645 [6, 3, 4, 2, 1, 5] (1,6,5)(2,3,4) %e A350645 [5, 6, 1, 2, 3, 4] (1,5,3)(2,6,4) %e A350645 [3, 4, 5, 6, 1, 2] (1,3,5)(2,4,6) %e A350645 [4, 3, 5, 6, 2, 1] (1,4,6)(2,3,5) %e A350645 [5, 3, 4, 2, 6, 1] (1,5,6)(2,3,4) %e A350645 [5, 4, 2, 3, 6, 1] (1,5,6)(2,4,3) . %Y A350645 Cf. A000108, A001006, A127632. %K A350645 nonn %O A350645 0,2 %A A350645 _Kassie Archer_, Jan 09 2022