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A301421
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Sums of positive coefficients of generalized Chebyshev polynomials of the first kind, for a family of 6 data.
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6
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1, 6, 46, 371, 3026, 24707, 201748, 1647429, 13452565, 109850886, 897019828, 7324880157, 59813470848, 488424550081, 3988374821616, 32568251770049, 265945672309613, 2171657880797162, 17733313387923690, 144806604435722311, 1182461068019218530, 9655734852907204771
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OFFSET
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1,2
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COMMENTS
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Re-express the Girard-Waring formulae to yield the mean powers in terms of the mean symmetric polynomials in the data values. Then for a family of 6 data, the sum of the positive coefficients in these polynomials is a(n). a(n+1)/a(n) approaches 1/(2^(1/6)-1). (For a family of 2 data, the coefficients of these polynomials give the Chebyshev polynomials of the first kind.) See extended comment in A301417.
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LINKS
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FORMULA
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G.f.: (-x*(x+1)^5+1)/(x^7+5*x^6+9*x^5+5*x^4-5*x^3-9*x^2-7*x+1); this denominator equals (1-x)*(2-(1+x)^6) (conjectured).
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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