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A125188
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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.
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1
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1, 1, 3, 12, 54, 259, 1294, 6655, 34986, 187149, 1015407, 5574829, 30915904, 172933249, 974605751, 5528804444, 31546576802, 180931023589, 1042503934315, 6031773336043, 35030156585236, 204135876541762, 1193291688154639
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..22.
A. Burstein, Restricted Dumont permutations, arXiv:math/0402378 [math.CO], 2004
A. Burstein, Restricted Dumont permutations, Annals of Combinatorics, 9, 2005, 269-280 (Theorem 3.13).
Matteo Cervetti and Luca Ferrari, Pattern avoidance in the matching pattern poset, arXiv:2009.01024 [math.CO], 2020.
Y. Sun and Z. Wang, Consecutive pattern avoidances in non-crossing trees, Graph. Combinat. 26 (2010) 815-832, G_{uud}
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FORMULA
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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
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A125187.
Sequence in context: A083881 A151208 A055835 * A054666 A006026 A158826
Adjacent sequences: A125185 A125186 A125187 * A125189 A125190 A125191
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Dec 19 2006
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STATUS
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approved
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