|
|
A073596
|
|
Expansion of exp(x)*log(1-x)/(x-1).
|
|
7
|
|
|
0, 1, 5, 23, 116, 669, 4429, 33375, 283072, 2673321, 27845293, 317274407, 3926774180, 52469606981, 752922837861, 11549166072847, 188596608142560, 3266826328953745, 59830416584102325, 1155208913864163511, 23453274942011893556, 499481183766226468013
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n) is the total number of cycles obtained by permuting the elements in every subset of {1,2,...,n}. - Geoffrey Critzer, Sep 24 2013
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ n! * exp(1) * (log(n) + gamma), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 02 2015
|
|
MAPLE
|
b:= proc(n) option remember; `if`(n<2, n, n*b(n-1)+(n-1)!) end:
a:= proc(n) add(b(k)*binomial(n, k), k=0..n) end:
|
|
MATHEMATICA
|
nn=19; Range[0, nn]!CoefficientList[Series[Exp[x]Log[1/(1-x)]/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Sep 24 2013 *)
|
|
PROG
|
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(exp(x)*log(1-x)/(x-1)))) \\ G. C. Greubel, Aug 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x)*Log(1-x)/(x-1))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Aug 28 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|