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A048608
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Denominators of coefficients in function a(x) such that a(a(x)) = ln(1+x).
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1
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1, 4, 48, 96, 3840, 30720, 13440, 2064384, 92897280, 594542592, 130799370240, 1121137459200, 40809403514880, 816188070297600, 48971284217856000, 5484783832399872000, 62160883433865216000, 1918107260244983808000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Recursion exists for coefficients, but is too complicated to use without a computer algebra system
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REFERENCES
| W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999
W. C. Yang, Composition equations, preprint, 1999
W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245.
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EXAMPLE
| x - x^2/4 + x^3 * 5/48 + ...
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MATHEMATICA
| n = 18 ;
a[x_] = Sum[c[k] k! x^k, {k, 1, n}];
sa = Series[a[x], {x, 0, n}];
coes = CoefficientList[ ComposeSeries[sa, sa] -
Series[Log[1+x], {x, 0, n}], x] // Rest ;
eq = Reduce[((# == 0) & /@ coes)];
Table[c[k] k!, {k, 1, n}] /. First[Solve[eq, Table[c[k], {k, 1, n}]]] // Denominator
(* Jean-François Alcover Mar 28 2011 + upgrading by Olivier Gerard *)
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CROSSREFS
| Cf. A048607.
Sequence in context: A010293 A178429 A157818 * A192418 A162673 A002287
Adjacent sequences: A048605 A048606 A048607 * A048609 A048610 A048611
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KEYWORD
| frac,nonn,nice
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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