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A135410
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a(n) = the 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, 2, 4, 10, 26, 80, 272, 1076, 4848, 24832, 142340, 902440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
The terms were calculated by R. J. Mathar (see link).
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LINKS
| R. J. Mathar, C== program
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EXAMPLE
| 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
| Sequence in context: A003239 A195924 A116673 * A148103 A148104 A179981
Adjacent sequences: A135407 A135408 A135409 * A135411 A135412 A135413
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KEYWORD
| more,nonn
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AUTHOR
| Leroy Quet Dec 10 2007
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