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Search: id:A120607
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| A120607 |
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G.f. satisfies: 37*A(x) = 36 + 81*x + A(x)^10, starting with [1,3,15]. |
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20
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| 1, 3, 15, 270, 5505, 124818, 3028200, 76896180, 2018211930, 54311811330, 1490518569747, 41556060361920, 1173726329836125, 33513124885393020, 965755118941566180, 28051840723006217040, 820439774630057541690
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OFFSET
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0,2
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COMMENT
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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
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G.f.: A(x) = 1 + Series_Reversion((1+37*x - (1+x)^10)/81). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(9*n,n)/(8*n+1) * (36+81*x)^(8*n+1)/37^(9*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + 3*x + 15*x^2 + 270*x^3 + 5505*x^4 + 124818*x^5 +...
A(x)^10 = 1 + 30*x + 555*x^2 + 9990*x^3 + 203685*x^4 + 4618266*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+3*x+15*x^2+x*O(x^n)); for(i=0, n, A=A+(-37*A+36+81*x+A^10)/27); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120606.
Sequence in context: A050474 A051179 A122591 this_sequence A013352 A013354 A013356
Adjacent sequences: A120604 A120605 A120606 this_sequence A120608 A120609 A120610
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2006
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