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Numerators of coefficients in function a(x) such that a(a(x)) = sinh(x).
2

%I #14 Apr 04 2014 04:36:26

%S 1,1,-1,53,-23,92713,-742031,-594673187,329366540401,-104491760828591,

%T 1508486324285153,582710832978168221,-1084662989735717135537,

%U 431265609837882130202597,784759327625761394688977441

%N Numerators of coefficients in function a(x) such that a(a(x)) = sinh(x).

%C A recursion exists for coefficients, but is too complicated to use without a computer algebra system.

%D W. C. Yang, Polynomials are essentially integer partitions, preprint, 1999

%D W. C. Yang, Composition equations, preprint, 1999

%H W. C. Yang, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00412-4">Derivatives are essentially integer partitions</a>, Discrete Math., 222 (2000), 235-245.

%e x + x^3/12 - x^5/160 + ...

%Y Cf. A048603. Apart from signs, the same sequence as A048602.

%K frac,sign,nice

%O 0,4

%A Winston C. Yang (yang(AT)math.wisc.edu)