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A292933
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E.g.f.: x/(x+3-2*exp(x)).
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5
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0, 1, 2, 12, 80, 690, 7092, 85162, 1168400, 18034938, 309307340, 5835250410, 120092842872, 2677545756106, 64289692962068, 1653899162167290, 45384277496827424, 1323216060906107994, 40848835928097158172, 1331096992220322502858
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) ~ n! / ((r-1) * (r-3)^n), where r = -LambertW(-1, -2*exp(-3)) = 3.5830738760366909976807989989303134394318270218566... - Vaclav Kotesovec, Sep 27 2017
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[x/(x+3-2Exp[x]), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 01 2019 *)
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PROG
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(PARI) concat(0, Vec(serlaplace(x/(x+3-2*exp(x))))) \\ Michel Marcus, Sep 27 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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