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 A212884 Number of permutations in S_n whose Rothe diagram can be rearranged to give the complement of a skew shape. 1
 1, 1, 2, 6, 24, 112, 572, 3116, 17871, 106959, 663526, 4243490, 27856087, 187029655, 1280660596, 8921737864, 63108620169, 452503644985, 3284213633684, 24098433889312, 178583179551488, 1335346240984360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equivalent definitions: (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. (2) Permutations that avoid the nine permutation patterns 24153, 25143, 31524, 31542, 32514, 32541, 42153, 52143, and 214365. LINKS Joel B. Lewis, Table of n, a(n) for n = 0..50 A. J. Klein, J. B. Lewis and A. H. Morales, Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams. FORMULA Ordinary g.f. is (1 - x)*V(x)^2 - V(x) + 1/(1 - x), where V(x) is the (ordinary) g.f. for A005802. CROSSREFS Sequence in context: A308726 A168490 A118376 * A085486 A152318 A152328 Adjacent sequences:  A212881 A212882 A212883 * A212885 A212886 A212887 KEYWORD nonn AUTHOR Joel B. Lewis, May 29 2012 STATUS approved

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Last modified January 27 09:09 EST 2020. Contains 331293 sequences. (Running on oeis4.)