1,2

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 7 data, the sum of the positive coefficients in these polynomials is a(n). a(n+1)/a(n) approaches 1/(2^(1/7)-1). (For a family of 2 data, the coefficients of these polynomials give the Chebyshev polynomials of the first kind.) The sums of the negative coefficients are 1 less than the corresponding sums of the positive coefficients. See extended comment in A301417.

G. G. Wojnar, D. S. Wojnar, and L. Q. Brin, Universal peculiar linear mean relationships in all polynomials, arXiv:1706.08381 [math.GM], 2017.

G.f.: (-x*(x+1)^6+1)/(x^2*(x^6+6*x^5+14*x^4+14*x^3-14*x-14)-8*x+1); this denominator equals (1-x)*(2-(1+x)^7) (conjectured).

(PARI) lista(7, nn) \\ use pari script file in A301417; Michel Marcus, Apr 21 2018

Cf. A302764, A024537, A195350, A301417, A301420, A301421.

Sequence in context: A098307 A055995 A387117 * A288690 A385514 A362726

Adjacent sequences: A301421 A301422 A301423 * A301425 A301426 A301427

Gregory Gerard Wojnar, Mar 20 2018

approved