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Search: id:A120600
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| A120600 |
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G.f. satisfies: 7*A(x) = 6 + x + A(x)^6, starting with [1,1,15]. |
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3
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| 1, 1, 15, 470, 18390, 805806, 37828981, 1860433080, 94614523740, 4935081398830, 262560448214031, 14193030016877406, 777315341935068820, 43039297954660894560, 2405249540028525971070, 135492504636185052358656
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OFFSET
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0,3
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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+7*x - (1+x)^6). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(6*n,n)/(5*n+1) * (6+x)^(5*n+1)/7^(6*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + x + 15*x^2 + 470*x^3 + 18390*x^4 + 805806*x^5 +...
A(x)^6 = 1 + 6*x + 105*x^2 + 3290*x^3 + 128730*x^4 + 5640642*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+15*x^2+x*O(x^n)); for(i=0, n, A=A-7*A+6+x+A^6); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120599, A120601 - A120607.
Sequence in context: A041420 A036506 A005815 this_sequence A129892 A079610 A013433
Adjacent sequences: A120597 A120598 A120599 this_sequence A120601 A120602 A120603
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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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