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Search: id:A052582
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| A052582 |
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A simple regular expression in a labeled universe. |
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+0
5
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| 0, 2, 8, 36, 192, 1200, 8640, 70560, 645120, 6531840, 72576000, 878169600, 11496038400, 161902540800, 2440992153600, 39230231040000, 669529276416000, 12093372555264000, 230485453406208000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Total number of pairs (a_i,a_(i+1)) in all permutations on [n] such that a_i,a_(i+1) are consecutive integers. - David Callan (callan(AT)stat.wisc.edu), Nov 04 2003
Number of permutations of {1,2,...,n+2} such that there is exactly one entry between the entries 1 and 2. Example: a(2)=8 because we have 1324, 1423, 2314, 2413, 3142, 4132, 3241, and 4231. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008
a(n)=A138770(n+2,1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2008
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 526
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FORMULA
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E.g.f.: 2*x/(-1+x)^2
Recurrence: {a(0)=0, a(1)=2, (-n^2-2*n-1)*a(n)+a(n+1)*n}
2*n*n!
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MAPLE
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spec := [S, {S=Prod(Sequence(Z), Sequence(Z), Union(Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Cf. A138770.
Sequence in context: A081958 A001540 A129044 this_sequence A020021 A052618 A055142
Adjacent sequences: A052579 A052580 A052581 this_sequence A052583 A052584 A052585
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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