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 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. 1
 1, 1, 3, 12, 54, 259, 1294, 6655, 34986, 187149, 1015407, 5574829, 30915904, 172933249, 974605751, 5528804444, 31546576802, 180931023589, 1042503934315, 6031773336043, 35030156585236, 204135876541762, 1193291688154639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES A. Burstein, Restricted Dumont permutations, Annals of Combinatorics, 9, 2005, 269-280 (Theorem 3.13). LINKS Y. Sun, Z. Wang, Consecutive pattern avoidances in non-crossing trees, Graph. Combinat. 26 (2010) 815-832, G_{uud} FORMULA 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. Conjecture: 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 a(n) ~ 5^(2*n+3/2) / (9 * 4^n * n^(3/2) * sqrt(3*Pi)). - Vaclav Kotesovec, Feb 03 2014 MAPLE 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); MATHEMATICA 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 *) CROSSREFS Cf. A125187. Sequence in context: A083881 A151208 A055835 * A054666 A006026 A158826 Adjacent sequences:  A125185 A125186 A125187 * A125189 A125190 A125191 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 19 2006 STATUS approved

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Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)