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Search: id:A120018
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| A120018 |
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The third self-composition of A120010; g.f.: A(x) = G(G(G(x))), where G(x) = g.f. of A120010. |
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+0
3
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| 1, 3, 9, 30, 114, 480, 2157, 10092, 48525, 238143, 1187952, 6006171, 30710553, 158535975, 825143145, 4325320191, 22814398392, 120999555588, 644878190175, 3451975941243, 18550877091063, 100047282676491, 541314936448764
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row 3 of A120019, the square table of self-compositions of A120010.
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FORMULA
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G.f.: A(x) = (1 - sqrt(1 - 4*x*(1-x)/(1-3*x+3*x^2) ))/2.
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EXAMPLE
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A(x) = x + 3*x^2 + 9*x^3 + 30*x^4 + 114*x^5 + 480*x^6 + 2157*x^7 +...
G(x) = x + x^2 + x^3 + 2*x^4 + 6*x^5 + 18*x^6 + 53*x^7 + 158*x^8 +...
where G(x) is the g.f. of A120010 and G(G(G(x))) = A(x).
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PROGRAM
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(PARI) {a(n)=polcoeff((1 - sqrt(1 - 4*x*(1-x)/(1-3*x+3*x^2+x*O(x^n)) ))/2, n)}
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CROSSREFS
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Cf. A120010, A120017 (2-nd self-composition), A120019.
Sequence in context: A134168 A124427 A055730 this_sequence A091353 A003604 A058148
Adjacent sequences: A120015 A120016 A120017 this_sequence A120019 A120020 A120021
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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 14 2006
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