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Search: id:A135801
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| A135801 |
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Fourth column (k=3) of triangle A134832 (circular succession numbers). |
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+0
2
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| 1, 0, 0, 20, 35, 448, 3024, 27480, 268125, 2905760, 34402368, 442140972, 6128803135, 91137168640, 1447072631840, 24433531297776, 437138635330137, 8260372499542080, 164393521482487360, 3436814164696775940
(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+3} with exactly three successor pairs (i,i+1). Due to cyclicity also (n+3,1) 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=3.
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FORMULA
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a(n)= binomial(n+3,3)*A000757(n), n>=0.
E.g.f.: diff(((x^3)/3!)*(1-ln(1-x))/e^x,x$3).
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EXAMPLE
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a(1)=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
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Cf. A134515 (column k=2). A135802 (column k=4).
Sequence in context: A024755 A048022 A048066 this_sequence A078210 A116657 A132606
Adjacent sequences: A135798 A135799 A135800 this_sequence A135802 A135803 A135804
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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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