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%I #17 Jun 17 2017 02:27:09
%S 1,1,1,1,2,1,1,5,5,1,1,14,33,14,1,1,42,234,238,42,1,1,132,1706,4146,
%T 1782,132,1
%N Square array read by antidiagonals downwards: T(n,k) = number of linear extensions of the North-East rectangular partial order NE_{n,k} that avoid the pattern 123.
%H David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, <a href="http://arxiv.org/abs/1605.06825">Pattern Avoiding Linear Extensions of Rectangular Posets</a>, arXiv preprint arXiv:1605.06825 [math.CO], 2016.
%e The square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 5, 14, 42, 132, ...
%e 1, 5, 33, 234, 1706, 12618, ...
%e 1, 14, 238, 4146, 72152, 126804, ...
%e 1, 42, 1782, 75187, 3099106, ...
%e 1, 132, 13593, 1378668, ...
%e 1, 429, 104756, 25430445, ...
%e ...
%e As a triangular array:
%e 1,
%e 1, 1,
%e 1, 2, 1,
%e 1, 5, 5, 1,
%e 1, 14, 33, 14, 1,
%e 1, 42, 234, 238, 42, 1,
%e 1, 132, 1706, 4146, 1782, 132, 1,
%e ...
%Y Cf. A281732, A281733, A281734.
%K nonn,tabl,more
%O 1,5
%A _N. J. A. Sloane_, Apr 07 2017
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