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A262973
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Total tail length of all iteration trajectories of all elements of random mappings from [n] to [n].
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2
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0, 2, 36, 624, 11800, 248400, 5817084, 150660608, 4285808496, 133010784000, 4475982692500, 162419627132928, 6324111407554824, 263067938335913984, 11645155099754347500, 546652030933421260800, 27126781579050558916576, 1418971858887930496745472
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OFFSET
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1,2
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COMMENTS
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An iteration trajectory is the directed graph obtained by iterating the mapping starting from one of the n elements until a cycle appears and consists of a tail attached to a cycle.
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LINKS
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FORMULA
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E.g.f.: T^2/(1-T)^4 where T is the labeled tree function, average over all mappings and values is asymptotic to sqrt(Pi*n/8).
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MAPLE
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proc(n) 1/2*n!*add(n^q*(n - q)*(n - 1 - q)/q!, q = 0 .. n - 2) end proc
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MATHEMATICA
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Table[n!/2 Sum[n^q (n - q) (n - 1 - q)/q!, {q, 0, n - 2}], {n, 21}] (* Michael De Vlieger, Oct 06 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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