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Search: id:A066165
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| A066165 |
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Variant of Stanley's children's game. Class of n (named) children forms into rings of at least two with exactly one child inside each ring. a(n) gives number of possibilities, including clockwise order (or which hand is held), in each ring. |
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+0
2
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| 3, 8, 30, 234, 1680, 13040, 119448, 1212120, 13412520, 161968872, 2118607920, 29813747040, 449227822680, 7216747374720, 123128587713600, 2223511629522624, 42370586275466880, 849664985938704000
(list; graph; listen)
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OFFSET
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3,1
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999 (Sec. 5.2)
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FORMULA
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E.g.f.: exp(-x*ln(1-x)-x^2)-1.
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EXAMPLE
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a(4)=8: ring must have 3 of the four, fourth in middle. Two ways for the three to hold hands.
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CROSSREFS
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Cf. A066166 (original version).
Sequence in context: A059171 A078619 A066304 this_sequence A119838 A108492 A003470
Adjacent sequences: A066162 A066163 A066164 this_sequence A066166 A066167 A066168
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 12 2001
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