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Search: id:A143340
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| A143340 |
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G.f. satisfies: A(x) = 1 + x*A(x)^3/A(-x). |
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+0
3
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| 1, 1, 4, 15, 84, 402, 2520, 13339, 88484, 494814, 3395816, 19657398, 137999048, 818024484, 5836517808, 35201610387, 254231733188, 1553691459558, 11327637588552, 69948932919906, 513856752260184, 3199802098978428
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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) - x*A(x)^3 = 1 + x^2*[A(x)*A(-x)]^2.
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EXAMPLE
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A bisection of g.f. A(x) equals a bisection of A(x)^3:
A(x) = 1 + x + 4*x^2 + 15*x^3 + 84*x^4 + 402*x^5 + 2520*x^6 + 13339*x^7 +...
A(x)^3 = 1 + 3*x + 15*x^2 + 70*x^3 + 402*x^4 + 2163*x^5 + 13339*x^6 +...
so that A(x) - x*A(x)^3 = 1 + x^2*[A(x)*A(-x)]^2, where
[A(x)*A(-x)]^2 = 1 + 14*x^2 + 357*x^4 + 11522*x^6 + 420170*x^8 +...
A(x)*A(-x) = 1 + 7*x^2 + 154*x^4 + 4683*x^6 + 165446*x^8 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*A^3/subst(A, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143339, A143341.
Sequence in context: A129653 A081722 A117927 this_sequence A151379 A130679 A107874
Adjacent sequences: A143337 A143338 A143339 this_sequence A143341 A143342 A143343
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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 09 2008
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