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A134515
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Third column (k=2) of triangle A134832 (circular succession numbers).
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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
| 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
| 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
| 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
| Cf. A135799 (column k=1).
Sequence in context: A056511 A166626 A114703 * A175335 A167788 A072968
Adjacent sequences: A134512 A134513 A134514 * A134516 A134517 A134518
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 21 2008, Feb 22 2008
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