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Search: id:A120597
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| A120597 |
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G.f. satisfies: 9*A(x) = 8 + 8*x + A(x)^5, starting with [1,2,10]. |
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+0
3
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| 1, 2, 10, 120, 1770, 29208, 516180, 9554640, 182867970, 3589443160, 71861735660, 1461730482160, 30123451315620, 627598216410480, 13197173403868200, 279728425129963680, 5970277970921643570, 128199003794219752920
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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+9*x - (1+x)^5)/8). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(5*n,n)/(4*n+1) * (8+8*x)^(4*n+1)/9^(5*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + 2*x + 10*x^2 + 120*x^3 + 1770*x^4 + 29208*x^5 +...
A(x)^5 = 1 + 10*x + 90*x^2 + 1080*x^3 + 15930*x^4 + 262872*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+2*x+10*x^2+x*O(x^n)); for(i=0, n, A=A+(-9*A+8+8*x+A^5)/4); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120596, A120598 - A120607.
Sequence in context: A131811 A006121 A110951 this_sequence A060690 A005617 A013038
Adjacent sequences: A120594 A120595 A120596 this_sequence A120598 A120599 A120600
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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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