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A009444
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E.g.f. log(1+x/exp(x)).
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0
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0, 1, -3, 11, -58, 409, -3606, 38149, -470856, 6641793, -105398650, 1858413061, -36044759796, 762659322385, -17481598316742, 431535346662645, -11413394655983536, 321989729198400385, -9651573930139850610
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 125
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FORMULA
| |a(n)| is asymptotic to (n-1)!/LambertW(1)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), 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)!), [From Vladimir Kruchinin, Oct 08 2011]
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MATHEMATICA
| Log[ 1+x/Exp[ x ] ]
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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); [From Vladimir Kruchinin, Oct 08 2011]
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CROSSREFS
| Sequence in context: A126201 A020012 A126100 * A168325 A141776 A071698
Adjacent sequences: A009441 A009442 A009443 * A009445 A009446 A009447
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
Definition corrected, Joerg Arndt, Apr 30 2011.
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