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A338368 Triangle of number of 312-avoiding reduced valid hook configurations with n hooks that are on permutations with 2n + k points, for n=1 and 1<=k<=n.

%I A338368 #5 Oct 23 2020 06:18:13
%S A338368 1,3,5,14,51,42,84,485,849,462,594,4743,13004,14819,6006,4719,48309,
%T A338368 182311,322789,271452,87516,40898,511607,2472322,5999489,7794646,
%U A338368 5182011,13856
%N A338368 Triangle of number of 312-avoiding reduced valid hook configurations with n hooks that are on permutations with 2n + k points, for n=1 and 1<=k<=n.
%H A338368 Ilani Axelrod-Freed, <a href="https://arxiv.org/abs/2010.11834">312-Avoiding Reduced Valid Hook Configurations and Duck Words</a>, arXiv:2010.11834 [math.CO], 2020.
%H A338368 Maya Sankar, <a href="https://arxiv.org/abs/1910.08895">Further Bijections to Pattern-Avoiding Valid Hook Configurations</a>, arXiv:1910.08895 [math.CO], 2019.
%e A338368 Triangle begins
%e A338368   1
%e A338368   3 5
%e A338368   14 51 42
%e A338368   84 485 849 462
%e A338368   594 4743 13004 14819 6006
%e A338368   4719 48309 182311 322789 271452 87516
%e A338368   40898 511607 2472322 5999489 7794646 5182011 13856
%Y A338368 Cf. A005700 (1st column), A005789 (right diagonal).
%K A338368 nonn,tabl,more
%O A338368 1,2
%A A338368 _Michel Marcus_, Oct 23 2020