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Search: id:A143342
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| A143342 |
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G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x). |
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+0
1
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| 1, 1, 6, 40, 374, 3215, 34298, 326360, 3710278, 37289620, 440121880, 4577214736, 55375589594, 589530372890, 7258264793564, 78597770766160, 980423896907046, 10754940952651740, 135521929778850952, 1501817992511869280
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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More generally, if A(x) = 1 + x*A(x)^n/A(-x)
then A(x) - x*A(x)^n = 1 + x^2*[A(x)*A(-x)]^(n-1)
so that a bisection of A(x) equals a bisection of A(x)^n.
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FORMULA
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G.f. satisfies: A(x) - x*A(x)^5 = 1 + x^2*[A(x)*A(-x)]^4.
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EXAMPLE
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A bisection of g.f. A(x) equals a bisection of A(x)^5:
A(x) = 1 + x + 6*x^2 + 40*x^3 + 374*x^4 + 3215*x^5 + 34298*x^6 + 326360*x^7 +...
A(x)^5 = 1 + 5*x + 40*x^2 + 330*x^3 + 3215*x^4 + 30756*x^5 + 326360*x^6 +...
so that A(x) - x*A(x)^5 = 1 + x^2*[A(x)*A(-x)]^4, where
[A(x)*A(-x)]^4 = 1 + 44*x^2 + 3542*x^4 + 358468*x^6 + 40846025*x^8 + +...
A(x)*A(-x) = 1 + 11*x^2 + 704*x^4 + 65054*x^6 + 7062088*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^5/subst(A, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143339, A143340, A143341.
Sequence in context: A006387 A014481 A000683 this_sequence A084270 A053677 A001367
Adjacent sequences: A143339 A143340 A143341 this_sequence A143343 A143344 A143345
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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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