A292934 E.g.f.: x^2/(x+3-2*exp(x)).

0, 0, 2, 6, 48, 400, 4140, 49644, 681296, 10515600, 180349380, 3402380740, 70023004920, 1561206957336, 37485640585484, 964345394431020, 26462386594676640, 771532717446066208, 23817889096309943892, 776127882633846005268

Offset: 0

Author

Jean-Luc Marichal, Sep 27 2017

Keywords

• nonn
• easy

Comments

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

Links

• M. Couceiro, J. Devillet, and J.-L. Marichal, Quasitrivial semigroups: characterizations and enumerations, arXiv:1709.09162 [math.RA], 2017.

Crossrefs

Cf. A292932, A292933.

Formula

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

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