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A140097
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G.f. satisfies: A(x) = Series_Reversion[ x/(1 + A(x) + A(x)^2) ].
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0
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1, 1, 3, 12, 60, 346, 2218, 15444, 115075, 908155, 7535185, 65374018, 590579575, 5537249212, 53742567000, 538801229874, 5570060420573, 59288164937748, 648934780013375, 7295904025820975, 84174136470742517, 995682428049720830
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| G.f. satisfies: A(x) = x*(1 + A(A(x)) + A(A(x))^2).
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EXAMPLE
| G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 60*x^5 + 346*x^6 + 2218*x^7 +...
A(A(x)) = x + 2*x^2 + 8*x^3 + 40*x^4 + 234*x^5 + 1526*x^6 +10816*x^7+...
A(A(x))^2 = x^2 + 4*x^3 + 20*x^4 + 112*x^5 + 692*x^6 + 4628*x^7 +...
x = A(x*[1 - A(x) + 2*A(x)^2 - 4*A(x)^3 + 9*A(x)^4 - 21*A(x)^5 +-...]).
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PROG
| (PARI) {a(n)=local(A=x); if(n<1, 0, for(i=1, n, A=serreverse(x/(1+A+A^2 +x*O(x^n)))); polcoeff(A, n))}
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CROSSREFS
| Cf. A001006 (Motzkin numbers).
Sequence in context: A181282 A020052 A096471 * A105227 A000258 A070863
Adjacent sequences: A140094 A140095 A140096 * A140098 A140099 A140100
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 15 2008
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