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 A318973 #14 Sep 15 2018 05:26:17 %S A318973 1,0,1,0,0,1,3,1,0,0,5,13,20,13,5,0,0,56,136,221,266,221,136,56,0,0, %T A318973 1092 %N A318973 Triangle read by rows: T(n,k) is the number of permutations of [2n-1] that have exactly one preimage under West's stack-sorting map and that also have first entry k. %C A318973 Rows are symmetric: T(n,k) = T(n,2n-k). %C A318973 It appears that the sequence T(n,1),...,T(n,2n-1) is always unimodal. In fact, it appears that this sequence is always log-concave. %C A318973 Row sums give A180874. %H A318973 Colin Defant, Michael Engen, and Jordan A. Miller, <a href="https://arxiv.org/abs/1809.01340">Stack-sorting, set partitions, and Lassalle's sequence</a>, arXiv:1809.01340 [math.CO], 2018. %F A318973 T(n,1) = T(n,2n-1) = 0 for n>1. %F A318973 T(n,2) = T(n,2n-2) = A180874(n-1) for n>1. %e A318973 The five uniquely sorted permutations of [5] are 21435, 31425, 32415, 32145, and 42135. Of these permutations, T(3,1) = 0 start with the entry 1, T(3,2) = 1 starts with 2, T(3,3) = 3 start with 3, T(3,4) = 1 starts with 4, and T(3,5) = 0 start with 5. %e A318973 Triangle begins: %e A318973 1, %e A318973 0, 1, 0, %e A318973 0, 1, 3, 1, 0, %e A318973 0, 5, 13, 20, 13, 5, 0, %e A318973 ... %Y A318973 Cf. A180874. %K A318973 nonn,tabf,more %O A318973 1,7 %A A318973 _Colin Defant_, Sep 06 2018