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%I #17 Nov 22 2023 07:33:08
%S 1,1,2,6,24,112,572,3116,17871,106959,663526,4243490,27856087,
%T 187029655,1280660596,8921737864,63108620169,452503644985,
%U 3284213633684,24098433889312,178583179551488,1335346240984360
%N Number of permutations in S_n whose Rothe diagram can be rearranged to give the complement of a skew shape.
%C Equivalent definitions:
%C (1) Permutations that have the form (a_1, a_2, ..., a_k, b_1, b_2, ..., b_(n - k)), where the subsequences (a_1, a_2, ..., a_k) and (b_1, b_2, ..., b_(n - k)) avoid the permutation pattern 2143 and a_i < b_j for all i, j.
%C (2) Permutations that avoid the nine permutation patterns 24153, 25143, 31524, 31542, 32514, 32541, 42153, 52143, and 214365.
%H Joel B. Lewis, <a href="/A212884/b212884.txt">Table of n, a(n) for n = 0..50</a>
%H A. J. Klein, J. B. Lewis and A. H. Morales, <a href="http://arxiv.org/abs/1203.5804">Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams</a>.
%H R. J. Mathar, <a href="/A212884/a212884.txt">D-finite recurrence</a>
%F Ordinary g.f. is (1 - x)*V(x)^2 - V(x) + 1/(1 - x), where V(x) is the (ordinary) g.f. for A005802.
%K nonn
%O 0,3
%A _Joel B. Lewis_, May 29 2012
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