%I #25 Oct 30 2022 08:59:47
%S 1,1,3,10,45,241,1525,11096,91441,842185,8577871,95768454,1163339221,
%T 15278140593,215739927481,3259925357716,52489756856993,
%U 897249441166993,16228613753092315,309660835748163394,6216734677256575581,130994769191324727697
%N Expansion of e.g.f. exp(x)*(1-x)^(-x).
%H Alois P. Heinz, <a href="/A184947/b184947.txt">Table of n, a(n) for n = 0..200</a>
%H Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties </a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F E.g.f.: exp(x)*(1-x)^(-x).
%F a(n) = sum(k=0..n, C(n,k) *sum(j=0..k, C(k,j) *abs(Stirling1(n-k,j)) *j!)).
%F a(n) ~ n! * exp(1). - _Vaclav Kotesovec_, Aug 13 2013
%p with(combinat):
%p a:= n-> add(binomial(n, k) *add(binomial(k, j)
%p *abs(stirling1(n-k, j)) *j!, j=0..k), k=0..n):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 03 2011
%t With[{nn=25},CoefficientList[Series[Exp[x](1-x)^-x,{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 26 2011 *)
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Feb 02 2011