OFFSET
1,2
COMMENTS
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.
LINKS
Gregory Gerard Wojnar, Table of n, a(n) for n = 1..62 [a(21) corrected by Georg Fischer, Aug 18 2021]
G. G. Wojnar, D. S. Wojnar, and L. Q. Brin, Universal peculiar linear mean relationships in all polynomials, arXiv:1706.08381 [math.GM], 2017. See Table GW.n=6 p. 24.
FORMULA
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).
PROG
(PARI) lista(6, nn) \\ use pari script file in A301417; Michel Marcus, Apr 21 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gregory Gerard Wojnar, Mar 20 2018
EXTENSIONS
a(21) corrected by Georg Fischer, Aug 18 2021
STATUS
approved