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A120601
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G.f. satisfies: 15*A(x) = 14 + 27*x + A(x)^6, starting with [1,3,15].
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2
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1, 3, 15, 210, 3510, 65562, 1310901, 27446760, 594104940, 13187589690, 298555767279, 6867021319722, 160017552201780, 3769622456958720, 89628027015591870, 2148034269252052608, 51836638064282565579
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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+15*x - (1+x)^6)/27). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(6*n,n)/(5*n+1) * (14+27*x)^(5*n+1)/15^(6*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
| A(x) = 1 + 3*x + 15*x^2 + 210*x^3 + 3510*x^4 + 65562*x^5 +...
A(x)^6 = 1 + 18*x + 225*x^2 + 3150*x^3 + 52650*x^4 + 983430*x^5 +...
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PROG
| (PARI) {a(n)=local(A=1+3*x+15*x^2+x*O(x^n)); for(i=0, n, A=A+(-15*A+14+27*x+A^6)/9); polcoeff(A, n)}
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CROSSREFS
| Cf. A120588 - A120600, A120602 - A120607.
Sequence in context: A166359 A195515 A003505 * A145272 A117820 A126453
Adjacent sequences: A120598 A120599 A120600 * A120602 A120603 A120604
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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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