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%I #7 Aug 21 2017 16:01:38
%S 1,0,2,9,8,130,1134,-252,29504,447480,-1837800,14172840,471846792,
%T -4864408848,14099478288,1166776034760,-18687216197760,31767501808320,
%U 5630793922569024,-113411010324632832,156669582211562880
%N E.g.f. (1+x+x^2)^(x+x^2)
%F a(n)=(sum(m=1..n, sum(k=m..n, (binomial(k,n-k)*stirling1(k-m,m))/(k-m)!)))*n!, n>0, a(0)=1.
%t With[{nn=20},CoefficientList[Series[(1+x+x^2)^(x+x^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 21 2017 *)
%o (Maxima)
%o a(n):=(sum(sum((binomial(k,n-k)*stirling1(k-m,m))/(k-m)!,k,m,n),m,1,n))*n!;
%K sign
%O 0,3
%A _Vladimir Kruchinin_, May 31 2011
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