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 A048608 Denominators of coefficients in function a(x) such that a(a(x)) = log(1+x). 1
 1, 4, 48, 96, 3840, 30720, 13440, 2064384, 92897280, 594542592, 130799370240, 1121137459200, 40809403514880, 816188070297600, 48971284217856000, 5484783832399872000, 62160883433865216000, 1918107260244983808000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A recursion exists for coefficients, but is too complicated to use without a computer algebra system. REFERENCES W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999 W. C. Yang, Composition equations, preprint, 1999 LINKS W. C. Yang, Derivatives are essentially integer partitions, Discrete Math., 222 (2000), 235-245. EXAMPLE x - x^2/4 + x^3 * 5/48 + ... 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 Gérard *) T[n_, m_] := T[n, m] = If[n == m, 1, (StirlingS1[n, m]*m!/n! - Sum[T[n, i]*T[i, m], {i, m+1, n-1}])/2]; a[n_] := T[n+1, 1] // Denominator; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Dec 16 2014, after Vladimir Kruchinin *) CROSSREFS Cf. A048607. Sequence in context: A178429 A242225 A157818 * A275033 A192418 A162673 Adjacent sequences:  A048605 A048606 A048607 * A048609 A048610 A048611 KEYWORD frac,nonn,nice AUTHOR Winston C. Yang (yang(AT)math.wisc.edu) STATUS approved

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Last modified January 21 20:10 EST 2019. Contains 319350 sequences. (Running on oeis4.)