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Search: id:A065513
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| A065513 |
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Number of endofunctions of [n] with a cycle a->b->c->a and for all x in [n], some iterate f^k(x)=a. |
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4
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| 2, 24, 300, 4320, 72030, 1376256, 29760696, 720000000, 19292299290, 567575838720, 18197320924068, 631732166467584, 23613833496093750, 945755921747804160, 40410678374256222960, 1835086247681868693504
(list; graph; listen)
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OFFSET
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3,1
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FORMULA
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E.g.f.: T^3/3 where T=T(x) is Euler's tree function (see A000169).
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EXAMPLE
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a(4)=24: 1->2->3->1<-4; 2->3->1->2<-4; 3->1->2->3<-4 1->3->2->1<-4; 3->2->1->3<-4; 2->1->3->2<-4 (repeat with 1,2, then 3 excluded from cycle)
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MAPLE
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T := x->-LambertW(-x); a := []; f := series((T(x))^3/3, x, 24); for m from 1 to 24 do a := [op(a), op(2*m-1, f)*(m+2)! ] od; print(a);
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CROSSREFS
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A000169 (unique cycle is length 1), A053506 (unique cycle has length 2)
Adjacent sequences: A065510 A065511 A065512 this_sequence A065514 A065515 A065516
Sequence in context: A065101 A052739 A135389 this_sequence A119491 A001864 A099045
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KEYWORD
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nonn
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 27 2001
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