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%I #7 Apr 01 2019 16:10:51
%S 1,0,2,3,20,-30,594,-840,14384,-167832,2300040,-17190360,153272712,
%T -2775904560,51294972624,-651268374120,7597950113280,-151775259773760,
%U 3587640413505984,-63586583168595840,972086975299451520
%N Expansion of e.g.f.: (1+x+x^2+x^3)^x
%F a(n)=(sum(m=1..n, sum(k=0..n-2*m, (stirling1(m+k,m)*sum(j=0..m+k, binomial(j,n-3*(m+k)-m+2*j)*binomial(m+k,j)))/(m+k)!)))*n!, n>0, a(0)=1.
%t With[{nn=30},CoefficientList[Series[(1+x+x^2+x^3)^x,{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Apr 01 2019 *)
%o (Maxima)
%o a(n):=(sum(sum((stirling1(m+k,m)*sum(binomial(j,n-3*(m+k)-m+2*j)*binomial(m+k,j),j,0,m+k))/(m+k)!,k,0,n-2*m),m,1,n))*n!;
%K sign
%O 0,3
%A _Vladimir Kruchinin_, Jun 02 2011
%E Definition clarified by _Harvey P. Dale_, Apr 01 2019
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