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Search: id:A135802
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| A135802 |
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Fifth column (k=4) of triangle A134832 (circular succession numbers). |
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3
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| 1, 0, 0, 35, 70, 1008, 7560, 75570, 804375, 9443720, 120408288, 1658028645, 24515212540, 387332966720, 6511826843280, 116059273664436, 2185693176650685, 43366955622595920, 904164368153680480
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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+4} with exactly four successor pairs (i,i+1). Due to cyclicity also (n+4,1) 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=4.
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FORMULA
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a(n)= binomial(n+4,4)*A000757(n), n>=0.
E.g.f.: diff(((x^4)/4!)*(1-ln(1-x))/e^x,x$4).
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EXAMPLE
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a(0)=1 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. Hence (1,2,3,4) is the only circular permutation with 4 successors.
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CROSSREFS
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Cf. A135801 (column k=3). A135803 (column k=5).
Sequence in context: A108172 A162832 A146207 this_sequence A043390 A031481 A044137
Adjacent sequences: A135799 A135800 A135801 this_sequence A135803 A135804 A135805
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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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