OFFSET
0,3
COMMENTS
It appears that a(n) is always positive for n > 9.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Branko Dragovich, On Summation of p-Adic Series, arXiv:1702.02569 [math.NT], 2017.
FORMULA
a(n) = Sum_{k=0..n} (-1)^k * A008275(k,n-k) n!/k!. - Max Alekseyev, Aug 10 2013
a(n) ~ 2 * n! / n^3 * (1 + (17/2-3*log(n)-3*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Apr 21 2014
MATHEMATICA
CoefficientList[Series[(1-x)^x, {x, 0, 30}], x]*Table[(n-1)!, {n, 1, 31}] (* Vincenzo Librandi, Jun 16 2012 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*stirling(k, n-k)*n!/k!) \\ Max Alekseyev, Aug 10 2013
(PARI) x='x+O('x^33); Vec(serlaplace(exp(x*log(1 - x)))) \\ Joerg Arndt, Apr 01 2017
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^x)); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 30 2018
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Signs from Christian G. Bower, Nov 15 1998
STATUS
approved