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%I M0601 #41 Sep 08 2022 08:44:35
%S 1,0,-2,-3,4,30,66,0,-496,-1512,1800,51480,487752,4633200,50605296,
%T 620703720,8278947840,118504008000,1811156124096,29452505385600,
%U 507926275873920,9260774050469760,178004846331607680,3597786477984061440,76284908749415574144,1693206585883612800000,39264054809925638534400
%N Expansion of e.g.f. (1 - x)^x.
%C It appears that a(n) is always positive for n > 9.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A007114/b007114.txt">Table of n, a(n) for n = 0..200</a>
%H Branko Dragovich, <a href="https://arxiv.org/abs/1702.02569">On Summation of p-Adic Series</a>, arXiv:1702.02569 [math.NT], 2017.
%F a(n) = Sum_{k=0..n} (-1)^k * A008275(k,n-k) n!/k!. - _Max Alekseyev_, Aug 10 2013
%F 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
%t CoefficientList[Series[(1-x)^x,{x,0,30}],x]*Table[(n-1)!,{n,1,31}] (* _Vincenzo Librandi_, Jun 16 2012 *)
%o (PARI) a(n) = sum(k=0,n, (-1)^k*stirling(k,n-k)*n!/k!) \\ _Max Alekseyev_, Aug 10 2013
%o (PARI) x='x+O('x^33); Vec(serlaplace(exp(x*log(1 - x)))) \\ _Joerg Arndt_, Apr 01 2017
%o (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
%K sign
%O 0,3
%A _Simon Plouffe_
%E Signs from _Christian G. Bower_, Nov 15 1998
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