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%I M0919 #37 Jun 06 2019 09:27:38
%S 1,0,2,-3,20,-90,594,-4200,34544,-316008,3207240,-35699400,432690312,
%T -5672581200,79991160144,-1207367605080,19423062612480,
%U -331770360922560,5997105160795584,-114373526841360000,2295170834453089920,-48344592370577247360
%N Expansion of e.g.f. (1 + x)^x.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
%H Vincenzo Librandi, <a href="/A007113/b007113.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=75">Encyclopedia of Combinatorial Structures 75</a>
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*k!*Stirling1(n-k, k). - _Vladeta Jovovic_, Dec 19 2004
%F a(n) ~ (-1)^n * n!. - _Vaclav Kotesovec_, Jun 06 2019
%p a:= n-> n! *coeff(series((1+x)^x, x, n+1), x, n):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Dec 12 2012
%t CoefficientList[Series[(1 + x)^x, {x, 0, 19}], x]*Table[(n - 1)!, {n, 1, 20}]
%t a[n_] := (-1)^n*n!*Sum[ StirlingS1[n - k, k]/(n - k)!*(-1)^(n - 2*k), {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Dec 12 2012, after _Vladeta Jovovic_ *)
%Y Cf. A053489, A053490. Apart from initial terms and signs, same as A066166.
%K sign
%O 0,3
%A _Simon Plouffe_
%E Signs from _Christian G. Bower_, Nov 15 1998
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