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A232607
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G.f. A(x) satisfies: (A(x) + x*A'(x)) / (A(x) - x*A(x)^2) = Sum_{n>=0} binomial(2*n,n)^2*x^n.
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3
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1, 3, 19, 159, 1546, 16517, 188246, 2248863, 27844369, 354576634, 4618570090, 61289049293, 826064774033, 11281763625102, 155834042142463, 2173801434825011, 30585769379262567, 433633765794690539, 6189637467948022825, 88886796123324352030, 1283443017706197910489, 18623352714450226405962
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: A(x) = (1/x)*Series_Reversion(x/F(x)) where F(x) = A(x/F(x)) is the g.f. of A232606.
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 19*x^2 + 159*x^3 + 1546*x^4 + 16517*x^5 + 188246*x^6 +...
where the g.f. satisfies:
(A(x) + x*A'(x)) / (A(x) - x*A(x)^2) = 1 + 2^2*x + 6^2*x^2 + 20^2*x^3 + 70^2*x^4 + 252^2*x^5 +...+ A000984(n)^2*x^n +...
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PROG
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(PARI) {a(n)=local(CB2=sum(k=0, n, binomial(2*k, k)^2*x^k)+x*O(x^n), A=1+x*O(x^n));
for(i=1, n, A = 1 + intformal( (CB2-1)*A/x - CB2*A^2)); polcoeff(A, n)}
for(n=0, 30, 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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