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 A306292 #17 Jun 03 2022 05:49:45
%S A306292 0,0,2,8,32,112,394,1360,4736,16544,58324,207088,741184,2671008,
%T A306292 9688410,35344800,129620480,477590080,1767170812,6563935664,
%U A306292 24465914304,91481858208,343058261572,1289901443168
%N A306292 Number of asymmetric Dyck paths of semilength n.
%C A306292 An asymmetric Dyck path is a path that generates a distinct Dyck path when traversed in opposite order.
%H A306292 J. Bonin, A. de Mier, and M. Noy, <a href="https://doi.org/10.1016/S0097-3165(03)00122-5">Lattice path matroids: enumerative aspects and Tutte polynomials</a>, J Comb Theory Ser A 104 (2003), 63-94.
%H A306292 L.-H. Deng, E. Y. P. Deng, and L. W. Shapiro, <a href="https://arxiv.org/abs/0906.1844">The Riordan group and symmetric lattice paths</a>, arXiv:0906.1844 [math.CO] (2009).
%H A306292 Zoe M. Himwich and Noah A. Rosenberg, <a href="https://arxiv.org/abs/1901.04465">Roadblocked monotonic paths and the enumeration of coalescent histories for non-matching caterpillar gene trees and species trees</a>, arXiv:1901.04465 [qbio.PE], 2019; Adv. Appl. Math. 113 (2020), 101939.
%F A306292 a(n) = (2n)! / (n! (n+1))! - n! / ( (floor(n/2))! (ceiling(n/2))! ).
%e A306292 For n=3, the a(2)=2 asymmetric Dyck paths are UUDDUD and UDUUDD.
%t A306292 Table[Binomial[2 n, n]/(n + 1) - Binomial[n, Floor[n/2]], {n, 0, 30}]
%o A306292 (PARI) a(n) = binomial(2*n, n)/(n+1) - binomial(n, n\2); \\ _Michel Marcus_, Jan 22 2020
%Y A306292 Equals twice A006079. Also A000108 minus A001405.
%K A306292 nonn
%O A306292 1,3
%A A306292 _Noah A Rosenberg_, Feb 04 2019