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Search: id:A135807
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| A135807 |
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Tenth column (k=9) of triangle A134832 (circular succession numbers). |
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+0
2
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| 1, 0, 0, 220, 715, 16016, 180180, 2619760, 39503750, 642172960, 11111964864, 204016477080, 3959206825210, 80952590044480, 1739019535313720, 39150661649469744, 921633956154372175, 22640304292494917600
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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+9} with exactly nine successor pairs (i,i+1). Due to cyclicity also (n+9,1) 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=9.
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FORMULA
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a(n)= binomial(n+9,9)*A000757(n), n>=0.
E.g.f.: diff(((x^9)/9!)*(1-ln(1-x))/e^x,x$9).
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EXAMPLE
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a(0)=1 because from the 9!/9=40320 circular permutations of n=9 elements only one, namely (1,2,3,4,5,6,7,8,9), has nine successors.
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CROSSREFS
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Cf. A135806 (column k=8).
Sequence in context: A121507 A063990 A157107 this_sequence A102073 A002025 A027797
Adjacent sequences: A135804 A135805 A135806 this_sequence A135808 A135809 A135810
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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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