|
|
A307006
|
|
Expansion of e.g.f. (2*exp(x)-1-2*x-x^2)/(1-x-x^2).
|
|
1
|
|
|
1, 1, 4, 20, 130, 1052, 10214, 115684, 1497458, 21806372, 352834942, 6279885284, 121932835754, 2564788969108, 58098821674742, 1410088008633812, 36505125340079074, 1004131069129741124, 29244927598399536878, 899066450011962665092, 29094401487631077315482, 988590340245276942963764
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of associative and quasitrivial binary operations on an n-element set that are order-preserving for some total ordering.
Convention a(0) = 1.
|
|
LINKS
|
|
|
FORMULA
|
Recurrence: a(1) = 1, a(2) = 4, a(n+2) = 2 + (n+2)*a(n+1) + (n+2)*(n+1)*a(n).
|
|
MATHEMATICA
|
Nest[Append[#1, 2 + #2 #1[[-1]] + #2 (#2 - 1) #1[[-2]] ] & @@ {#, Length@ #} &, {1, 1, 4}, 19] (* Michael De Vlieger, Apr 21 2019 *)
With[{nn=30}, CoefficientList[Series[(2Exp[x]-1-2x-x^2)/(1-x-x^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 12 2020 *)
|
|
PROG
|
(PARI) my(x='x+O('x^30)); Vec(serlaplace((2*exp(x)-1-2*x-x^2)/(1-x-x^2))) \\ Felix Fröhlich, Mar 19 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|