

A262973


Total tail length of all iteration trajectories of all elements of random mappings from [n] to [n].


0



0, 2, 36, 624, 11800, 248400, 5817084, 150660608, 4285808496, 133010784000, 4475982692500, 162419627132928, 6324111407554824, 263067938335913984, 11645155099754347500, 546652030933421260800, 27126781579050558916576, 1418971858887930496745472
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OFFSET

1,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..18.
P. Flajolet and A. M. Odlyzko, Random Mapping Statistics, INRIA RR 1114, 1989.
Math StackExchange, Generating functions for tail length and rholength


FORMULA

E.g.f: T^2/(1T)^4 where T is the labeled tree function, average over all mappings and values is asymptotic to sqrt(Pi*n/8).


MAPLE

proc(n) 1/2*n!*add(n^q*(n  q)*(n  1  q)/q!, q = 0 .. n  2) end proc


MATHEMATICA

Table[n!/2 Sum[n^q (n  q) (n  1  q)/q!, {q, 0, n  2}], {n, 21}] (* Michael De Vlieger, Oct 06 2015 *)


CROSSREFS

Sequence in context: A064030 A228790 A124104 * A207832 A112036 A093530
Adjacent sequences: A262970 A262971 A262972 * A262974 A262975 A262976


KEYWORD

nonn


AUTHOR

Marko Riedel, Oct 05 2015


STATUS

approved



