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A135410
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Number of permutations of {1,2,3,...,n} each with the same up-down signature as its inverse permutation.
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1
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1, 1, 2, 4, 10, 26, 80, 272, 1076, 4848, 24832, 142340, 902440, 6257264, 47042924, 380800060, 3300070116, 30472353884, 298595442140
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OFFSET
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0,3
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COMMENTS
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An "up-down signature" of the permutation (p(1),p(2),p(3),...,p(n)) is the sequence of (n-1) signs (+ or -) where the k-th sign in the sequence is the sign of (p(k+1)-p(k)). All permutations of {1,2,3,...,n} which are their own inverses obviously have the same up-down signature as their inverse permutations.
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LINKS
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EXAMPLE
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The up-down signature of the permutation (4,2,6,3,5,1) is -+-+-. This permutation's inverse permutation is (6,2,4,1,5,3). The inverse permutation also has the up-down signature -+-+-. So these two permutations, among others, are included in the count for n = 6.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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