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
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
KEYWORD
nonn,easy
AUTHOR
J. Devillet, May 22 2019
STATUS
approved