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Search: id:A121687
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| A121687 |
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G.f. satisfies: A(x) = 1 + x*A(x) * A( x*A(x) )^2. |
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+0
2
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| 1, 1, 3, 14, 83, 574, 4432, 37244, 335153, 3194510, 32001596, 335019839, 3649450270, 41227610316, 481724831132, 5809341783543, 72177761136925, 922539273876404, 12115001489115910, 163284755614174305
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. satisfies: G(x) = x/(1 + x*A(x)^2) where G(x*A(x)) = x.
G.f. satisfies: A(x) = 1/(1 - x*A(x*A(x))^2).
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EXAMPLE
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G.f. A(x) = 1 + x + 3*x^2 + 14*x^3 + 83*x^4 + 574*x^5 + 4432*x^6 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 34*x^3 + 203*x^4 + 1398*x^5 + 10706*x^6 +...
A(x*A(x)) = 1 + x + 4*x^2 + 23*x^3 + 160*x^4 + 1259*x^5 + 10833*x^6 +...
A(x*A(x))^2 = 1 + 2*x + 9*x^2 + 54*x^3 + 382*x^4 + 3022*x^5 + 25993*x^6 +...
A(x)*A(x*A(x))^2 = 1 + 3*x + 14*x^2 + 83*x^3 + 574*x^4 + 4432*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=0, n, A=serreverse(x/(1+x*(A +x*O(x^n))^2))/x); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A^2, x, x*A))); polcoef f(A, n)}
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CROSSREFS
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Adjacent sequences: A121684 A121685 A121686 this_sequence A121688 A121689 A121690
Sequence in context: A032080 A020104 A103467 this_sequence A154757 A074535 A005700
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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), Aug 15 2006, Aug 20 2008
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