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Search: id:A135803
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| A135803 |
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Sixth column (k=5) of triangle A134832 (circular succession numbers). |
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+0
3
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| 1, 0, 0, 56, 126, 2016, 16632, 181368, 2091375, 26442416, 361224864, 5305691664, 83351722636, 1394398680192, 24744942004464, 464237094657744, 9179911341932877, 190814604739422048, 4159156093506930208
(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+5} with exactly five successor pairs (i,i+1). Due to cyclicity also (n+5,1) 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=5.
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FORMULA
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a(n)= binomial(n+5,5)*A000757(n), n>=0.
E.g.f.: diff(((x^5)/5!)*(1-ln(1-x))/e^x,x$5).
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EXAMPLE
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a(0)=1 because from the 5!/5=24 circular permutations of n=5 elements only one, namely (1,2,3,4,5), has five successors.
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CROSSREFS
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Cf. A135802 (column k=4). A135804 (column k=6).
Sequence in context: A038849 A003781 A030443 this_sequence A048452 A121736 A107937
Adjacent sequences: A135800 A135801 A135802 this_sequence A135804 A135805 A135806
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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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