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 A123922 #14 Jul 27 2018 14:47:11
%S A123922 1,1,2,6,21,84,360,1650,7865,39039,198744,1039584,5534928,30046752,
%T A123922 165257136,922280634,5199131025,29644168125,170375955750,988180543350,
%U A123922 5768664340725,33927954699600,200617471267200,1193673954039840
%N A123922 Number of 2143-avoiding Dumont paths of the 2nd kind of length 2n.
%H A123922 A. Burstein, S. Elizalde and T. Mansour, <a href="https://arxiv.org/abs/math/0610234">Restricted Dumont Permutations, Dyck Paths and Noncrossing Partitions</a>, arXiv:math/0610234 [math.CO], 2006.
%F A123922 a(n) = A047749(n)*A047749(n+1).
%F A123922 Conjecture: 16*n*(n+2)*(n+1)^2*a(n) -108*n*(n+1)*(2*n-1)*a(n-1) -9*(3*n-5)*(3*n-1)*(3*n-4)*(3*n-2)*a(n-2)=0. - _R. J. Mathar_, Jan 25 2013
%e A123922 For n=2, there are 3 Dumont permutations of the 2nd kind of length 2n=4, namely {2143,3142,4132}.
%e A123922 Avoiding 2143, the cardinality of this set is reduced to a(2)=2.
%t A123922 b[n_] := If[EvenQ[n], Binomial[3n/2, n/2]/(n+1), Binomial[(3n-1)/2, (n+1)/2 ]/n];
%t A123922 a[n_] := b[n] b[n+1];
%t A123922 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jul 27 2018 *)
%o A123922 (PARI) A047749(n)={ my(m=floor(n/2)); if(n % 2, binomial(3*m+1,m+1)/(2*m+1), binomial(3*m,m)/(2*m+1)); }
%o A123922 a(n)={ A047749(n)*A047749(n+1); }
%Y A123922 Cf. A001469, A047749.
%K A123922 easy,nonn
%O A123922 0,3
%A A123922 _R. J. Mathar_, Nov 20 2006