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 A262970 Total cycle length of all iteration trajectories of all elements of random mappings from [n] to [n]. 1
 1, 10, 117, 1648, 27425, 528336, 11581885, 284878336, 7772592897, 233010784000, 7614411069221, 269412832512000, 10261487793254113, 418636033893726208, 18213563455467238125, 841799936112774086656, 41189866031118283907585, 2127207204243268173103104 (list; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Table of n, a(n) for n = 1..380 P. Flajolet and A. M. Odlyzko, Random Mapping Statistics, INRIA RR 1114, 1989. Math StackExchange, Generating functions for tail length and rho-length FORMULA E.g.f.: T/(1-T)^4, where T is the labeled tree function, average over all mappings and values asymptotic to sqrt(Pi*n/8). MAPLE proc(n) 1/2*n!*add(n^q*(n + 1 - q)*(n - q)/q!, q = 0 .. n - 1) end proc MATHEMATICA Table[n!/2 Sum[n^q (n + 1 - q) (n - q)/q!, {q, 0, n - 1}], {n, 21}] (* Michael De Vlieger, Oct 06 2015 *) PROG (PARI) a(n) = n! * sum(q=0, n-1, n^q*(n+1-q)*(n-q)/q!)/2; CROSSREFS Sequence in context: A251318 A083448 A024129 * A309582 A155622 A307695 Adjacent sequences:  A262967 A262968 A262969 * A262971 A262972 A262973 KEYWORD nonn AUTHOR Marko Riedel, Oct 05 2015 STATUS approved

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Last modified October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)