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A209519
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Expansion A(x) = Sum_{n>0} a(n)*x^n/(3^(n-1)*n!), A(x) satisfies A(A(A(x)))=e^x-1.
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4
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1, 1, 0, 0, 2, -21, 138, 150, -22833, 303975, 3451320, -214016553, 666006714, 228865308144, -4943013567642, -396567325158381, 21423378444873687, 1022158819761317838, -121532275123709160942
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OFFSET
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1,5
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LINKS
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FORMULA
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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.
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PROG
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(Maxima)
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));
makelist(n!*3^(n-1)*(T(n, 1)), n, 1, 7);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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