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%I #7 Dec 25 2023 18:11:39
%S 1,1,0,0,2,-21,138,150,-22833,303975,3451320,-214016553,666006714,
%T 228865308144,-4943013567642,-396567325158381,21423378444873687,
%U 1022158819761317838,-121532275123709160942
%N Expansion A(x) = Sum_{n>0} a(n)*x^n/(3^(n-1)*n!), A(x) satisfies A(A(A(x)))=e^x-1.
%F a(n)=3^(n-1)*n!*T(n,1), T(n,m)=1/3*(stirling2(n,m)*m!/n!-sum(k=m+1..n-1, T(k,m)*sum(i=k..n, T(n,i)*T(i,k)))-T(m,m)*sum(i=m+1..n-1, T(n,i)*T(i,m))), n>m, T(n,n)=1.
%o (Maxima)
%o T(n,m):=if n=m then 1 else 1/3*(stirling2(n,m)*m!/n!-sum(T(k,m)*sum(T(n,i)*T(i,k),i,k,n),k,m+1,n-1)-T(m,m)*sum(T(n,i)*T(i,m),i,m+1,n-1));
%o makelist(n!*3^(n-1)*(T(n,1)),n,1,7);
%K sign
%O 1,5
%A _Vladimir Kruchinin_, Mar 10 2012
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