OFFSET
1,2
COMMENTS
Number of k-ary associative and quasitrivial operations that have no neutral element 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) ~ n! * (4-r) / ((r-1) * (r-3)^(n+1)), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 2019
E.g.f.: (1 - x)/(x + 3 - 2*exp(x)). - Andrew Howroyd, Aug 19 2019
MATHEMATICA
nmax = 20; Rest[CoefficientList[Series[(1 - x)/(3 - 2*E^x + x), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *)
PROG
(PARI) seq(n)={Vec(-1+serlaplace((1-x)/(x+3-2*exp(x))) + O(x*x^n), -n)} \\ Andrew Howroyd, Aug 19 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. Devillet, May 21 2019
STATUS
approved