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 A007767 #83 Jan 02 2025 22:20:08
%S A007767 1,1,3,17,151,1899,31711,672697,17551323,549500451,20246665349,
%T A007767 864261579999,42190730051687,2329965898878307,144220683681814515,
%U A007767 9926440976428215117,754465679498026783923,62939664181821196179459,5732069150321309755351161,567176164248814234096702451
%N A007767 Number of pairs of permutations of degree n that avoid (12,21).
%C A007767 A pair of permutations (p,q) of degree n avoid (12,21) if there do not exist indices 1<=i<j<=n such that p_i < p_j and q_j < q_i. - _Noam Zeilberger_, Jun 06 2016 (via Steve Linton)
%C A007767 Number of intervals (i.e. ordered pairs (x,y) such that x<=y) in the permutation lattice of size n, that is, pairs of permutations (x,y) related by the weak Bruhat order x<=y iff inversions(x) is a subset of inversions(y) (see Hammett and Pittel, p. 4567). - _Noam Zeilberger_, Jun 01 2016
%H A007767 Andrew Elvey Price, <a href="/A007767/b007767.txt">Table of n, a(n) for n = 0..26</a>
%H A007767 Noga Alon, Kirill Rudov, and Leeat Yariv, <a href="https://lyariv.mycpanel.princeton.edu/papers/DominanceSolvability.pdf">Dominance Solvability in Random Games</a>, Princeton Univ. (2020).
%H A007767 Noga Alon, Kirill Rudov, and Leeat Yariv, <a href="https://lyariv.mycpanel.princeton.edu/papers/DominanceSolvabilityAppendix.pdf">Online Appendix for 'Dominance Solvability in Random Games'</a>, Princeton Univ. (2021).
%H A007767 Grégory Chatel, Vincent Pilaud, and Viviane Pons, <a href="https://arxiv.org/abs/1701.07995">The weak order on integer posets</a>, arXiv:1701.07995 [math.CO], 2017.
%H A007767 Clément Chenevière, <a href="https://theses.hal.science/tel-04255439">Enumerative study of intervals in lattices of Tamari type</a>, Ph. D. thesis, Univ. Strasbourg (France), Ruhr-Univ. Bochum (Germany), HAL tel-04255439 [math.CO], 2024. See pp. 3, 33, 145.
%H A007767 Joël Gay and Vincent Pilaud, <a href="https://arxiv.org/abs/1804.06572">The weak order on Weyl posets</a>, arXiv:1804.06572 [math.CO], 2018.
%H A007767 Benjamin Gunby, <a href="https://arxiv.org/abs/1609.06023">Asymptotics of Pattern Avoidance in the Permutation-Tuple and Klazar Set Partition Settings</a>, arXiv:1609.06023 [math.CO], 2017.
%H A007767 Adam Hammett and Boris Pittel, <a href="http://dx.doi.org/10.1090/S0002-9947-08-04478-4">How often are two permutations comparable?</a>, Transactions of the AMS 360:9 (2008), 4541-4568.
%H A007767 Evgeny Kapun, <a href="/A007767/a007767.java.txt">Java program for generating terms a(0)-a(13)</a>.
%F A007767 a(n) = Sum_{k=1..n!} k * A263754(n,k). - _Alois P. Heinz_, Jun 06 2016
%o A007767 (Java) // See Kapun link.
%Y A007767 Cf. A000260, A263754.
%K A007767 nonn
%O A007767 0,3
%A A007767 _Steve Linton_
%E A007767 a(0)=1 prepended by _Alois P. Heinz_, Jun 06 2016
%E A007767 a(10)-a(13) from _Evgeny Kapun_, Dec 11 2016
%E A007767 More terms from _Andrew Elvey Price_, Feb 08 2024