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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

Table of n, a(n) for n=0..18.

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

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

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

Definition corrected by Joerg Arndt, Apr 30 2011

STATUS

approved

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Last modified September 23 17:50 EDT 2017. Contains 292363 sequences.