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A218801
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G.f. A(x) satisfies: 1+x = Sum_{n>=0} n^n*x^n*A(-n*x)^n/n! * exp(-n*x*A(-n*x)).
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0
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1, 1, 5, 60, 1539, 82539, 9208086, 2123763546, 1005501106845, 971130952310487, 1903911554135421599, 7548458861108146087406, 60351476147380872012216644, 971005203586845989294297793744, 31389082794561063490845804374258994, 2036350822333032259401319084453988921002
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OFFSET
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0,3
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COMMENTS
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Compare to the identity: 1/(1-x) = Sum_{n>=0} n^n*x^n/n! * exp(-n*x).
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + 5*x^2 + 60*x^3 + 1539*x^4 + 82539*x^5 + 9208086*x^6 +...
where
1+x = 1 + x*A(-x)*exp(-x*A(-x)) + 2^2*x^2*A(-2*x)^2/2!*exp(-2*x*A(-2*x)) + 3^3*x^3*A(-3*x)^3/3!*exp(-3*x*A(-3*x)) + 4^4*x^4*A(-4*x)^4/4!*exp(-4*x*A(-4*x)) +...
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PROG
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(PARI) a(n)=local(A=1+x+sum(k=2, n-1, a(k)*x^k)+x^2*O(x^n)); if(n<2, 1, -(-1)^n*polcoeff(sum(k=0, n+2, k^k*x^k*subst(A, x, -k*x)^k/k!*exp(-k*x*subst(A, x, -k*x)+x^2*O(x^n))), n+1))
for(n=0, 15, print1(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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