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A141382
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G.f. satisfies: A(x) = x + A(A(A(A(x)))^2).
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3
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1, 1, 6, 58, 702, 9830, 152632, 2565042, 45938878, 867667140, 17154629472, 353091007048, 7534733877540, 166160874412976, 3777158124019664, 88326122515058436, 2121170864722835600, 52242518805270485716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| G.f. satisfies: A( x - A(A(A(x))^2) ) = x.
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EXAMPLE
| G.f.: A(x) = x + x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 14*x^3 + 147*x^4 + 1890*x^5 + 27732*x^6 +...
A(A(A(x))) = x + 3*x^2 + 24*x^3 + 273*x^4 + 3730*x^5 + 57488*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 36*x^3 + 442*x^4 + 6412*x^5 + 103890*x^6 +...
A(A(A(A(x)))^2) = x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
The series reversion of A(x) = x - A(A(A(x))^2), where
A(A(A(x))^2) = x^2 + 4*x^3 + 33*x^4 + 358*x^5 + 4650*x^6 + 68168*x^7 +...
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PROG
| (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, subst(A^2, x, subst(A, x, A+x*O(x^n))))); polcoeff(A, n)}
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CROSSREFS
| Cf. A141380, A141381, A141383; A141371.
Sequence in context: A184708 A004301 A073848 * A034982 A156147 A024269
Adjacent sequences: A141379 A141380 A141381 * A141383 A141384 A141385
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008
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