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A143739
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G.f. A(x) satisfies: A(x) = (1-x)^3*A(x)^2 - x^2*A'(x).
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0
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1, 3, 9, 28, 90, 300, 1051, 3975, 16971, 86584, 550560, 4354308, 41245021, 448722207, 5443128597, 72294557416, 1039558994214, 16059538853232, 264996063891607, 4648786414414347, 86363450200625247, 1693336666564186012
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..21.
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 300*x^5 + 1051*x^6 +...
A(x)^2 = 1 + 6*x + 27*x^2 + 110*x^3 + 429*x^4 + 1644*x^5 + 6306*x^6 +...
(1-x)^3*A(x)^2 = 1 + 3*x + 12*x^2 + 46*x^3 + 174*x^4 + 660*x^5 +...
x^2*A'(x) = 3*x^2 + 18*x^3 + 84*x^4 + 360*x^5 + 1500*x^6 + 6306*x^7 +...
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=(1+x^2*deriv(A)/A)/(1-x)^3); polcoeff(A, n)}
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CROSSREFS
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Cf. A137553 (variant).
Sequence in context: A033190 A071724 A000245 * A189940 A047047 A071744
Adjacent sequences: A143736 A143737 A143738 * A143740 A143741 A143742
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Sep 05 2008
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STATUS
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approved
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