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Search: id:A141202
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| A141202 |
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G.f. satisfies: A(x + A(x)*A(-x)) = x. |
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+0
1
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| 1, 1, 2, 8, 32, 178, 944, 6255, 39366, 293652, 2090576, 17085798, 134136792, 1182991528, 10085875720, 95087538324, 871536657504, 8727880568468, 85385942061016, 904071273001352, 9389429908430784, 104728235042891360
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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G.f. satisfies: A(x) = x - A(-A(x))*A(A(x)).
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EXAMPLE
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By definition, Series_Reversion(A(x)) = x + A(-x)*A(x) where
A(-x)*A(x) = -x^2 -3*x^4 -52*x^6 -1596*x^8 -68174*x^10 -3679964*x^12-..
Consequently, A(x) = x - A(-A(x))*A(A(x)) where
-A(-A(x)) = x + 0*x^2 + 2*x^3 + x^4 + 30*x^5 + 38*x^6 + 852*x^7 +...
G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 32*x^5 + 178*x^6 + 944*x^7 +...
The series reversion of A(x) = x + A(x)*A(-x), thus:
A(x - x^2 - 3*x^4 - 52*x^6 - 1596*x^8 - 68174*x^10 -...) = x.
A(A(x)) = x + 2*x^2 + 6*x^3 + 27*x^4 + 134*x^5 + 786*x^6 + 4852*x^7 +...
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PROGRAM
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(PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=serreverse(x+A*subst(A, x, -x+x*O(x^n)))) ; polcoeff(A, n)}
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CROSSREFS
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Sequence in context: A051636 A081561 A009753 this_sequence A081358 A048855 A062797
Adjacent sequences: A141199 A141200 A141201 this_sequence A141203 A141204 A141205
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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 13 2008, Sep 05 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 13 2008 at the suggestion of R. J. Mathar
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