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Search: id:A134515
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| A134515 |
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Third column (k=2) of triangle A134832 (circular succession numbers). |
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+0
3
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| 1, 0, 0, 10, 15, 168, 1008, 8244, 73125, 726440, 7939008, 94744494, 1225760627, 17088219120, 255365758560, 4072255216296, 69021889788969, 1239055874931312, 23484788783212480, 468656477004105810, 9821896865573503095
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n) enumerates circular permutations of {1,2,...,n+2} with exactly two successor pairs (i,i+1). Due to cyclicity also (n+2,1) is a successor pair.
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REFERENCES
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Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 183, eq. (5.15), for k=2.
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FORMULA
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E.g.f.: diff(((x^2)/2!)*(1-ln(1-x))/e^x,x$2).
a(n)= (((n+2)*(n+1))/2)*A000757(n), n>=0.
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EXAMPLE
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a(2)=0 because the 4!/4=6 circular permutations of n=4 elements (1,2,3,4), (1,4,3,2), (1,3,4,2),(1,2,4,3), (1,4,2,3), and (1,3,2,4) have 4,0,1,1,1, and 1 successor pair, respectively.
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CROSSREFS
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Cf. A135799 (column k=1).
Adjacent sequences: A134512 A134513 A134514 this_sequence A134516 A134517 A134518
Sequence in context: A056522 A056511 A114703 this_sequence A072968 A072138 A109891
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008, Feb 22 2008
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