|
| |
|
|
A308352
|
|
Number of k-ary quasitrivial semigroups that have no neutral element on an n-element set.
|
|
2
|
|
|
|
0, 2, 8, 58, 492, 5074, 60888, 835482, 12895796, 221169970, 4172486496, 85872215290, 1914575169756, 45970251182418, 1182618181384424, 32451961380002458, 946163712877067460, 29208900504551394610, 951798961321369842864, 32647628386008050898810
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Number of k-ary associative and quasitrivial operations that have no neutral element on an n-element set.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) ~ n! * (4-r) / ((r-1) * (r-3)^(n+1)), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 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
|
|
|
|
STATUS
|
approved
|
| |
|
|
