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A221835
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G.f. satisfies: A(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + A(-x)^k).
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0
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1, 1, 1, 1, 2, 2, 5, 7, 23, 48, 190, 469, 2076, 5613, 27112, 80004, 415821, 1332560, 7380671, 25483465, 149401274, 552137511, 3408722899, 13414205244, 86845091349, 362317409552, 2451291749604, 10800354549538, 76134098052646, 353054546986058, 2586405677507199
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OFFSET
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0,5
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COMMENTS
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Compare to the identity:
G(x) = Sum_{n>=0} x^n / Product_{k=1..n} (x + G(-k*x)) when G(x) = 1/(1-x).
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 2*x^5 + 5*x^6 + 7*x^7 + 23*x^8 +...
where
A(x) = 1 + x/(x+A(-x)) + x^2/((x+A(-x))*(x+A(-x)^2)) + x^3/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)) + x^4/((x+A(-x))*(x+A(-x)^2)*(x+A(-x)^3)*(x+A(-x)^4)) +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/prod(k=1, m, x+subst(A^k, x, -x+x*O(x^n))) )); polcoeff(A, n)}
for(n=0, 40, 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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