A292933 E.g.f.: x/(x+3-2*exp(x)).

0, 1, 2, 12, 80, 690, 7092, 85162, 1168400, 18034938, 309307340, 5835250410, 120092842872, 2677545756106, 64289692962068, 1653899162167290, 45384277496827424, 1323216060906107994, 40848835928097158172, 1331096992220322502858

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 neutral elements. Also: Number of associative and quasitrivial binary operations on {1,...,n} that have 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, A292934.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[x/(x+3-2Exp[x]),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 01 2019 *)

PARI

concat(0, Vec(serlaplace(x/(x+3-2*exp(x))))) \\ Michel Marcus, Sep 27 2017

Formula

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

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