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%I #15 Aug 30 2018 17:29:01
%S 1,18,305,5595,113974,2581964,64727522,1783995060,53705023251,
%T 1755078270264,61920105083187,2346728722199680,95117694573257784,
%U 4106779625155078528,188206877039146217476,9125798298446360109312,466820173490890114763781,25126459591455539907002880
%N Number of endofunctions on [n] with exactly three cycles.
%H Alois P. Heinz, <a href="/A273434/b273434.txt">Table of n, a(n) for n = 3..386</a>
%F E.g.f.: -1/6 * log(1+LambertW(-x))^3.
%F a(n) ~ n^(n-1/2) * sqrt(2*Pi) * (log(n))^2 / 16 * (1 + 2*(gamma - log(2))/log(n) + (gamma^2 - 2*log(2)*gamma + log(2)^2 - Pi^2/6)/log(n)^2), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Nov 01 2016
%t Drop[CoefficientList[Series[-1/6 * Log[1+LambertW[-x]]^3, {x, 0, 20}], x] * Range[0, 20]!, 3] (* _Vaclav Kotesovec_, Nov 01 2016 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(-log(1+lambertw(-x))^3/6)) \\ _G. C. Greubel_, Aug 30 2018
%Y Column k=3 of A060281.
%K nonn
%O 3,2
%A _Alois P. Heinz_, May 22 2016