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A195895
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E.g.f. satisfies: A(x) = exp(-1) * Sum_{n>=0} exp(x*A(x)^n)/n!.
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4
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1, 1, 3, 19, 201, 2996, 57613, 1357987, 37921761, 1224420067, 44884358461, 1841710133330, 83634349451425, 4164470926316377, 225629247763909837, 13214729079087267931, 831997985912417838017, 56038514134260089791916, 4020820086886704204188797
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f. satisfies: A(x) = Sum_{n>=0} exp(A(x)^n - 1)*x^n/n!. [From Paul D. Hanna, Sep 27 2011]
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 201*x^4/4! + 2996*x^5/5! +...
where
A(x) = exp(-1)*(exp(x) + exp(x*A(x)) + exp(x*A(x)^2)/2! + exp(x*A(x)^3)/3! +...).
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(-1)*sum(m=0, 2*n+10, exp(x*A^m+x*O(x^n))/m!)); round(n!*polcoeff(A, n))}
(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, exp(A^m-1)*X^m/m!)); n!*polcoeff(A, n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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