login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009444 E.g.f. log(1 + x*exp(-x)). 3
0, 1, -3, 11, -58, 409, -3606, 38149, -470856, 6641793, -105398650, 1858413061, -36044759796, 762659322385, -17481598316742, 431535346662645, -11413394655983536, 321989729198400385, -9651573930139850610 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

abs(a(n)) is the number of connected functions f:{1,2,...,n}->{1,2,...,n} such that every element is mapped into a recurrent element. Cf. A006153. - Geoffrey Critzer, May 24 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 125

FORMULA

abs(a(n)) is asymptotic to (n-1)!/LambertW(1)^n. - Vladeta Jovovic, Jul 12 2007

Sequence of absolute values has e.g.f. log(1/(1-x*exp(x))). - Joerg Arndt, Apr 30 2011

a(n) = (-1)^(n+1)*n!*sum(m=1..n, m^(n-m-1)/(n-m)!). - Vladimir Kruchinin, Oct 08 2011

MATHEMATICA

With[{nmax = 40}, CoefficientList[Series[Log[1 + x*Exp[-x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 22 2017 *)

PROG

(PARI) x='x+O('x^66); /* that many terms */

egf=1/(1+x/exp(x)); /* = 1 - x + 2*x^2 - 7/2*x^3 + 37/6*x^4 - 87/8*x^5 +... */

Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 30 2011 */

(Maxima)

a(n):=(-1)^(n+1)*n!*sum(m^(n-m-1)/(n-m)!, m, 1, n); /* Vladimir Kruchinin, Oct 08 2011 */

(Sage)

A009444 = lambda n: (-1)^(n+1)*factorial(n)*sum(m^(n-m-1)/factorial(n-m) for m in (1..n))

[A009444(n) for n in (0..9)] # Peter Luschny, Jan 18 2016

CROSSREFS

Cf. A006153.

Sequence in context: A208990 A020012 A126100 * A168325 A141776 A071698

Adjacent sequences:  A009441 A009442 A009443 * A009445 A009446 A009447

KEYWORD

sign,easy,changed

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

Definition corrected by Joerg Arndt, Apr 30 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 22 09:35 EST 2017. Contains 295076 sequences.