|
|
A273434
|
|
Number of endofunctions on [n] with exactly three cycles.
|
|
2
|
|
|
1, 18, 305, 5595, 113974, 2581964, 64727522, 1783995060, 53705023251, 1755078270264, 61920105083187, 2346728722199680, 95117694573257784, 4106779625155078528, 188206877039146217476, 9125798298446360109312, 466820173490890114763781, 25126459591455539907002880
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,2
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: -1/6 * log(1+LambertW(-x))^3.
a(n) ~ n^(n-1/2) * sqrt(2*Pi) * (log(n))^2 / 16 * (1 + 2*(gamma - log(2))/log(n) + (gamma^2 - 2*log(2)*gamma + log(2)^2 - Pi^2/6)/log(n)^2), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Nov 01 2016
|
|
MATHEMATICA
|
Drop[CoefficientList[Series[-1/6 * Log[1+LambertW[-x]]^3, {x, 0, 20}], x] * Range[0, 20]!, 3] (* Vaclav Kotesovec, Nov 01 2016 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(-log(1+lambertw(-x))^3/6)) \\ G. C. Greubel, Aug 30 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|