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%I #35 Jan 04 2021 19:28:46
%S 0,2,36,624,11800,248400,5817084,150660608,4285808496,133010784000,
%T 4475982692500,162419627132928,6324111407554824,263067938335913984,
%U 11645155099754347500,546652030933421260800,27126781579050558916576,1418971858887930496745472
%N Total tail length of all iteration trajectories of all elements of random mappings from [n] to [n].
%C 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.
%H G. C. Greubel, <a href="/A262973/b262973.txt">Table of n, a(n) for n = 1..380</a>
%H P. Flajolet and A. M. Odlyzko, <a href="https://hal.inria.fr/inria-00075445">Random Mapping Statistics</a>, INRIA RR 1114, 1989.
%H Math StackExchange, <a href="http://math.stackexchange.com/questions/1463544/">Generating functions for tail length and rho-length</a>
%F 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).
%p proc(n) 1/2*n!*add(n^q*(n - q)*(n - 1 - q)/q!, q = 0 .. n - 2) end proc
%t Table[n!/2 Sum[n^q (n - q) (n - 1 - q)/q!, {q, 0, n - 2}], {n, 21}] (* _Michael De Vlieger_, Oct 06 2015 *)
%K nonn
%O 1,2
%A _Marko Riedel_, Oct 05 2015
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