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A120606
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G.f. satisfies: 36*A(x) = 35 + 81*x + A(x)^9, starting with [1,3,12].
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2
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1, 3, 12, 180, 3018, 56238, 1121484, 23406804, 504914175, 11167352013, 251879507880, 5771456609880, 133970974830420, 3143760834627420, 74454455230816008, 1777349666975945784, 42721359085344132657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
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FORMULA
| G.f.: A(x) = 1 + Series_Reversion((1+36*x - (1+x)^9)/81). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(9*n,n)/(8*n+1) * (35+81*x)^(8*n+1)/36^(9*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
| A(x) = 1 + 3*x + 12*x^2 + 180*x^3 + 3018*x^4 + 56238*x^5 +...
A(x)^9 = 1 + 27*x + 432*x^2 + 6480*x^3 + 108648*x^4 + 2024568*x^5 +...
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PROG
| (PARI) {a(n)=local(A=1+3*x+12*x^2+x*O(x^n)); for(i=0, n, A=A+(-36*A+35+81*x+A^9)/27); polcoeff(A, n)}
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CROSSREFS
| Cf. A120588 - A120605, A120607.
Sequence in context: A028301 A004168 A061960 * A089428 A063801 A160320
Adjacent sequences: A120603 A120604 A120605 * A120607 A120608 A120609
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2006
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