A308362 Number of (2k+1)-ary quasitrivial semigroups on an n-element set.

1, 5, 23, 162, 1382, 14236, 170872, 2344530, 36188534, 620652000, 11708927276, 240976560622, 5372724404530, 129002764437228, 3318690040767224, 91067432174168202, 2655146132506208558, 81966680980803524728, 2670959894858615348356, 91616517379045122841830

Offset

1,2

Comments

Number of (2k+1)-ary associative and quasitrivial operations on an n-element set.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..413

M. Couceiro, J. Devillet, All quasitrivial n-ary semigroups are reducible to semigroups, arXiv:1904.05968 [math.RA], 2019.

Jimmy Devillet, Miguel Couceiro, Characterizations and enumerations of classes of quasitrivial n-ary semigroups, 98th Workshop on General Algebra (AAA98, Dresden, Germany 2019).

Formula

a(n) = A308352(n) + A292933(n) + A308354(n) for n >= 1.

a(n) = A292932(n) + binomial(n,2)*A292932(n-2) for n >= 2.

E.g.f.: (2 + x^2)/(6 - 4*exp(x) + 2*x). - Vaclav Kotesovec, Jun 05 2019

a(n) ~ n! * (r^2 - 6*r + 11) / (2*(r-1) * (r-3)^(n+1)), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 2019

Mathematica

nmax = 20; Rest[CoefficientList[Series[(2 + x^2)/(6 - 4*E^x + 2*x), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *)

Crossrefs

Cf. A308352, A308354, A292932, A292933.

Sequence in context: A336183 A342196 A228851 * A054749 A107204 A178383

Adjacent sequences: A308359 A308360 A308361 * A308363 A308364 A308365

Keyword

nonn,easy

Author

J. Devillet, May 22 2019

Status

approved