cp's OEIS Frontend

A125188 Number of Dumont permutations of the first kind of length 2n avoiding the patterns 2413 and 4132. Also number of Dumont permutations of the first kind of length 2n avoiding the patterns 1423 and 3142.

%I A125188 #21 Sep 14 2022 16:51:10
%S A125188 1,1,3,12,54,259,1294,6655,34986,187149,1015407,5574829,30915904,
%T A125188 172933249,974605751,5528804444,31546576802,180931023589,
%U A125188 1042503934315,6031773336043,35030156585236,204135876541762,1193291688154639
%N A125188 Number of Dumont permutations of the first kind of length 2n avoiding the patterns 2413 and 4132. Also number of Dumont permutations of the first kind of length 2n avoiding the patterns 1423 and 3142.
%H A125188 A. Burstein, <a href="http://arxiv.org/abs/math/0402378">Restricted Dumont permutations</a>, arXiv:math/0402378 [math.CO], 2004
%H A125188 A. Burstein, <a href="http://dx.doi.org/10.1007/s00026-005-0256-4">Restricted Dumont permutations</a>, Annals of Combinatorics, 9, 2005, 269-280 (Theorem 3.13).
%H A125188 Matteo Cervetti and Luca Ferrari, <a href="https://arxiv.org/abs/2009.01024">Pattern avoidance in the matching pattern poset</a>, arXiv:2009.01024 [math.CO], 2020.
%H A125188 Matteo Cervetti and Luca Ferrari, <a href="https://doi.org/10.1007/s00026-022-00596-1">Enumeration of Some Classes of Pattern Avoiding Matchings, with a Glimpse into the Matching Pattern Poset</a>, Annals of Combinatorics (2022).
%H A125188 Y. Sun and Z. Wang, <a href="http://dx.doi.org/10.1007/s00373-010-0950-9">Consecutive pattern avoidances in non-crossing trees</a>, Graph. Combinat. 26 (2010) 815-832, G_{uud}
%F A125188 G.f.=[1+xC(x)-sqrt(1-xC(x)-5x)]/[2x(1+C(x))], where C(x)=(1-sqrt(1-4x))/(2x) is the Catalan function.
%F A125188 D-finite with recurrence 32*(n-1)*(2*n-1)*(n+1)*a(n) +8*(-148*n^3+461*n^2-367*n+14)*a(n-1) +4*(2197*n^3-13436*n^2+25653*n-14694)*a(n-2) +2*(-16868*n^3+159415*n^2-483427*n+468080)*a(n-3) +(66623*n^3-867526*n^2+3651197*n-4985254)*a(n-4) -20*(2*n-9)*(1027*n^2-13868*n+42561)*a(n-5) -10500*(n-5)*(2*n-9)*(2*n-11)*a(n-6)=0. - _R. J. Mathar_, Jul 27 2013
%F A125188 a(n) ~ 5^(2*n+3/2) / (9 * 4^n * n^(3/2) * sqrt(3*Pi)). - _Vaclav Kotesovec_, Feb 03 2014
%p A125188 C:=(1-sqrt(1-4*x))/2/x: G:=(1+x*C-sqrt(1-x*C-5*x))/2/x/(1+C): Gser:=series(G,x=0,30): seq(coeff(Gser,x,n),n=0..26);
%t A125188 CoefficientList[Series[(-3+Sqrt[2]*Sqrt[1+Sqrt[1-4*x]-10*x] + Sqrt[1-4*x])/(2*(-1+Sqrt[1-4*x]-2*x)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 03 2014 *)
%Y A125188 Cf. A125187.
%K A125188 nonn
%O A125188 0,3
%A A125188 _Emeric Deutsch_, Dec 19 2006