OFFSET
1,3
COMMENTS
Number of (2k+1)-ary associative and quasitrivial operations that have two neutral elements 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) = binomial(n,2)*A292932(n-2) for n >= 2.
E.g.f.: x^2/(3 - 2*exp(x) + x)/2. - Vaclav Kotesovec, Jun 05 2019
a(n) ~ n! / (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[x^2/(3 - 2*E^x + x)/2, {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. Devillet, May 21 2019
STATUS
approved