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%I #11 Jun 24 2019 04:38:09
%S 1,1,2,7,36,239,1892,17015,168503,1799272,20409644
%N Number of Dumont permutations of the first kind of length 2n avoiding pattern 2143 (or pattern 3421).
%C Conjecture: The number of Dumont permutations of the first kind avoiding pattern 2143 equals the number of Dumont permutations of the first kind avoiding pattern 3421 for all n >= 0.
%C Data for n=7,8,9,10 is due to _Michael Albert_.
%D O. Jones, Enumeration of Dumont permutations avoiding certain four-letter patterns, Ph.D. thesis, Howard University, 2019.
%H D. Dumont, <a href="http://dx.doi.org/10.1215/S0012-7094-74-04134-9">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318.
%e For n=3, the 7 Dumont permutations of the first kind avoiding pattern 2143 are 356421, 364215, 435621, 563421, 564213, 634215, 642135, and the 7 Dumont permutations of the first kind avoiding pattern 3421 are 214365, 216435, 421365, 421563, 421635, 621435, 642135.
%Y Cf. A001469, A110501.
%K nonn,more
%O 0,3
%A _Alexander Burstein_ and _Opel Jones_, Jun 21 2019
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