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Search: id:A120605
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| A120605 |
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G.f. satisfies: 25*A(x) = 24 + 64*x + A(x)^9, starting with [1,4,36]. |
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+0
3
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| 1, 4, 36, 984, 31716, 1140552, 43895208, 1768717872, 73674176868, 3146885203432, 137085166193976, 6066992348458704, 272023207778276136, 12330039492509279184, 564072488005316830416, 26010805156782400648800
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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+25*x - (1+x)^9)/64). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(9*n,n)/(8*n+1) * (24+64*x)^(8*n+1)/25^(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 + 4*x + 36*x^2 + 984*x^3 + 31716*x^4 + 1140552*x^5 +...
A(x)^9 = 1 + 36*x + 900*x^2 + 24600*x^3 + 792900*x^4 + 28513800*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+4*x+36*x^2+x*O(x^n)); for(i=0, n, A=A+(-25*A+24+64*x+A^9)/16); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120604, A120606, A120607.
Sequence in context: A127901 A061742 A136469 this_sequence A143764 A152287 A086857
Adjacent sequences: A120602 A120603 A120604 this_sequence A120606 A120607 A120608
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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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