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Search: id:A143556
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| A143556 |
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G.f. satisfies: A(x) = 1 + x*A(x)^3/A(-x)^3. |
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+0
5
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| 1, 1, 6, 18, 110, 498, 3366, 17282, 122958, 672930, 4938758, 28103730, 210595182, 1230391058, 9358456230, 55727128866, 428643977422, 2589488117826, 20092671283974, 122759098980690, 959216278565742, 5913900861617970
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OFFSET
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0,3
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FORMULA
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G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).
G.f. satisfies: (A(x) - 1)^2 = ( 1 - (1+x^2)/A(x) )^3/x = x^2*A(x)^6/A(-x)^6.
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EXAMPLE
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G.f. A(x) = 1 + x + 6*x^2 + 18*x^3 + 110*x^4 + 498*x^5 + 3366*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 26*x^3 + 50*x^4 + 706*x^5 + 1650*x^6 +...
A(x)^2/A(-x)^2 = 1 + 4*x + 8*x^2 + 60*x^3 + 208*x^4 + 1716*x^5 +...
where 1 - (1+x^2)/A(x) = x*A(x)^2/A(-x)^2.
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PROGRAM
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^3/subst(A^3, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143555, A143557, A143558, A143559.
Sequence in context: A009573 A052655 A108735 this_sequence A007126 A009576 A009580
Adjacent sequences: A143553 A143554 A143555 this_sequence A143557 A143558 A143559
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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 24 2008
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