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Search: id:A066166
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| A066166 |
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Stanley's children's game. Class of n (named) children forms into rings with exactly one child inside each ring. We allow the case when outer ring has only one child. a(n) gives number of possibilities, including clockwise order (or which hand is held), in each ring. |
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+0
3
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| 2, 3, 20, 90, 594, 4200, 34544, 316008, 3207240, 35699400, 432690312, 5672581200, 79991160144, 1207367605080, 19423062612480, 331770360922560, 5997105160795584, 114373526841360000, 2295170834453089920
(list; graph; listen)
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OFFSET
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2,1
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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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LINKS
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P. Flajolet, S. Gerhold and B. Salvy, On the non-holonomic character of logarithms, powers and the n-th prime function
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FORMULA
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E.g.f.: -1+1/(1-x)^x.
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EXAMPLE
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a(4)=20: 12 ways to make 2 hugs, 8 ways to make a 3-ring.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*polcoeff(-1+1/(1-x+x*O(x^n))^x, n))
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CROSSREFS
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Cf. A066165. Apart from initial terms and signs, same as A007113.
Sequence in context: A041567 A087301 A007113 this_sequence A052804 A125763 A042441
Adjacent sequences: A066163 A066164 A066165 this_sequence A066167 A066168 A066169
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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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