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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
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.
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 * A375923 A085486 A152318
KEYWORD
nonn
AUTHOR
Joel B. Lewis, May 29 2012
STATUS
approved