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E.g.f.: x^2/(x+3-2*exp(x)).
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%I #11 Sep 27 2017 09:19:17

%S 0,0,2,6,48,400,4140,49644,681296,10515600,180349380,3402380740,

%T 70023004920,1561206957336,37485640585484,964345394431020,

%U 26462386594676640,771532717446066208,23817889096309943892,776127882633846005268

%N E.g.f.: x^2/(x+3-2*exp(x)).

%C Number of associative and quasitrivial binary operations on {1,...,n} that have both neutral and annihilator elements.

%H M. Couceiro, J. Devillet, and J.-L. Marichal, <a href="http://arxiv.org/abs/1709.09162">Quasitrivial semigroups: characterizations and enumerations</a>, arXiv:1709.09162 [math.RA], 2017.

%F a(n) = n*(n-1)*A292932(n-2).

%F a(n) ~ n! / ((r-1) * (r-3)^(n-1)), where r = -LambertW(-1, -2*exp(-3)) = 3.5830738760366909976807989989303134394318270218566... - _Vaclav Kotesovec_, Sep 27 2017

%Y Cf. A292932, A292933.

%K nonn,easy

%O 0,3

%A _Jean-Luc Marichal_, Sep 27 2017