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A112806
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Expansion of solution of functional equation.
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1
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1, 1, 2, 6, 21, 79, 312, 1277, 5369, 23049, 100612, 445214, 1992606, 9004260, 41025315, 188259072, 869305315, 4036286518, 18832973733, 88259024068, 415252542641, 1960718710035, 9288106921038, 44129146527731
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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Given g.f. A(x), then series reversion of B(x)=x*A(x^3) is -B(-x).
Given g.f. A(x), then y=x*A(x^3) satisfies y=x+(xy)^2/(1-(xy)^3).
G.f. satisfies: A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^3). - Paul D. Hanna, Jun 06 2012
G.f. satisfies: A(x) = 1/A(-x*A(x)^3); note that the Catalan function C(x) = 1 + x*C(x)^2 (A000108) also satisfies this condition. - Paul D. Hanna, Jun 06 2012
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PROG
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(PARI) {a(n)=local(A); if(n<0, 0, A=x+O(x^4); for(k=1, n, A=x+subst(x^2/(1-x^3), x, x*A)); polcoeff(A, 3*n+1))}
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*A^2/(1-x^2*A^3)); polcoeff(A, n)} \\ Paul D. Hanna, Jun 06 2012
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CROSSREFS
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Cf. A216490.
Sequence in context: A150198 A033321 A050203 * A150199 A150200 A150201
Adjacent sequences: A112803 A112804 A112805 * A112807 A112808 A112809
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 20 2005
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STATUS
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approved
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