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A359553
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Numerator of the coefficient of x^(2n+1) in the Taylor series expansion of sin(sin(x)).
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3
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1, -1, 1, -8, 13, -47, 15481, -15788, 451939, -23252857, 186846623, -831520891, 1108990801, -143356511198507, 920716137922619, -13390469094133441, 929480267163260699, -118186323448146684881, 69875813865886026036091, -155759565768613453511731
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OFFSET
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0,4
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COMMENTS
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Sine is an odd function so the Taylor series has 0 coefficients at even terms x^(2n).
A003712(n) is the numerator for use with denominator (2n+1)! so that here a(n)/A359554(n) = A003712(n)/(2n+1)! reduced to least terms.
abs(a(n)) is the corresponding numerator in the expansion of sinh(sinh(x)).
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LINKS
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FORMULA
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a(n) = numerator of A003712(n)/(2n+1)!.
Sum_{n>=0} a(n)/A359554(n) * x^(2*n+1). = sin(sin(x)).
Sum_{n>=0} abs(a(n))/A359554(n) * x^(2*n+1). = sinh(sinh(x)).
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EXAMPLE
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Fractions begin: 1, -1/3, 1/10, -8/315, 13/2520, -47/49896, ...
Series begins: sin(sin(x)) = x - (1/3)*x^3 + (1/10)*x^5 - (8/315)*x^7 + ...
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PROG
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(PARI) a_vector(len) = apply(numerator, Vec(substpol(sin(sin(Ser('x, , 2*len)))/'x, 'x^2, 'x)));
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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STATUS
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approved
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