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A145349
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G.f. satisfies: A(x/A(x)^3) = 1 + x*A(x).
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1
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1, 1, 4, 34, 416, 6319, 111124, 2177346, 46440184, 1061938195, 25762345804, 658072997702, 17600573291712, 490770914734054, 14219015899154068, 426904437068035200, 13252855203929697200, 424634035832800883743
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: A(x) = 1 + x*G(x)^4 where G(x) = A(x*G(x)^3) and A(x) = G(x/A(x)^3).
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EXAMPLE
| G.f.: A(x) = 1 + x + 4*x^2 + 34*x^3 + 416*x^4 + 6319*x^5 +...
A(x)^3 = 1 + 3*x + 15*x^2 + 127*x^3 + 1512*x^4 + 22419*x^5 +...
A(x/A(x)^3) = 1 + x + x^2 + 4*x^3 + 34*x^4 + 416*x^5 + 6319*x^6 +...
A(x) = 1 + x*G(x)^4 where G(x) = A(x*G(x)^3):
G(x) = 1 + x + 7*x^2 + 82*x^3 + 1239*x^4 + 21942*x^5 + 434746*x^6 +...
G(x)^3 = 1 + 3*x + 24*x^2 + 289*x^3 + 4377*x^4 + 77097*x^5 +...
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PROG
| (PARI) {a(n)=local(A=1+x, G); for(i=0, n, G=(serreverse(x/(A+x*O(x^n))^3)/x)^(1/3); A=1+x*G^4); polcoeff(A, n)}
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CROSSREFS
| Cf. variants: A002293, A145347, A145348, A120974.
Sequence in context: A197065 A141007 A158839 * A052630 A071213 A052629
Adjacent sequences: A145346 A145347 A145348 * A145350 A145351 A145352
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 11 2008
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