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Search: id:A135806
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| A135806 |
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Ninth column (k=8) of triangle A134832 (circular succession numbers). |
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+0
3
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| 1, 0, 0, 165, 495, 10296, 108108, 1473615, 20913750, 321086480, 5263562304, 91807414686, 1696802925090, 33116968654560, 680485905122760, 14681498118551154, 331788224215573983, 7837028408940548400
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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+8} with exactly eight successor pairs (i,i+1). Due to cyclicity also (n+8,1) 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=8.
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FORMULA
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a(n)= binomial(n+8,8)*A000757(n), n>=0.
E.g.f.: diff(((x^8)/8!)*(1-ln(1-x))/e^x,x$8).
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EXAMPLE
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a(0)=1 because from the 8!/8=5040 circular permutations of n=8 elements only one, namely (1,2,3,4,5,6,7,8), has eight successors.
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CROSSREFS
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Cf. A135805 (column k=7). A135807 (column k=9).
Sequence in context: A035826 A083255 A029563 this_sequence A124409 A066177 A027796
Adjacent sequences: A135803 A135804 A135805 this_sequence A135807 A135808 A135809
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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
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