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Search: id:A141372
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| A141372 |
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G.f. satisfies: A(x) = x + A(A(A(x)))^2. |
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+0
4
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| 1, 1, 6, 57, 684, 9512, 146848, 2455208, 43764802, 822963750, 16203122280, 332189276516, 7062047285812, 155178233311932, 3515420453148936, 81936668615592785, 1961578144170589430, 48167700575393576406
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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 - A(A(x))^2 ) = x.
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EXAMPLE
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G.f.: A(x) = x + x^2 + 6*x^3 + 57*x^4 + 684*x^5 + 9512*x^6 +...
A(A(x)) = x + 2*x^2 + 14*x^3 + 145*x^4 + 1848*x^5 + 26920*x^6 +...
A(A(A(x))) = x + 3*x^2 + 24*x^3 + 270*x^4 + 3658*x^5 + 55970*x^6 +...
A(A(A(x)))^2 = x^2 + 6*x^3 + 57*x^4 + 684*x^5 + 9512*x^6 +...
The series reversion of A(x) = x - A(A(x))^2, where
A(A(x))^2 = x^2 + 4*x^3 + 32*x^4 + 346*x^5 + 4472*x^6 + 65292*x^7 +...
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PROGRAM
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(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A^2, x, subst(A, x, A+x*O(x^n)))); polcoeff(A, n)}
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CROSSREFS
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Cf. A141370, A141371.
Sequence in context: A130565 A124556 A060435 this_sequence A087659 A107718 A000406
Adjacent sequences: A141369 A141370 A141371 this_sequence A141373 A141374 A141375
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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 28 2008
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