cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A301421 Sums of positive coefficients of generalized Chebyshev polynomials of the first kind, for a family of 6 data.

This page as a plain text file.
%I A301421 #30 Aug 18 2021 15:27:07
%S A301421 1,6,46,371,3026,24707,201748,1647429,13452565,109850886,897019828,
%T A301421 7324880157,59813470848,488424550081,3988374821616,32568251770049,
%U A301421 265945672309613,2171657880797162,17733313387923690,144806604435722311,1182461068019218530,9655734852907204771
%N A301421 Sums of positive coefficients of generalized Chebyshev polynomials of the first kind, for a family of 6 data.
%C A301421 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.
%H A301421 Gregory Gerard Wojnar, <a href="/A301421/b301421.txt">Table of n, a(n) for n = 1..62</a> [a(21) corrected by _Georg Fischer_, Aug 18 2021]
%H A301421 G. G. Wojnar, D. S. Wojnar, and L. Q. Brin, <a href="http://arxiv.org/abs/1706.08381">Universal peculiar linear mean relationships in all polynomials</a>, arXiv:1706.08381 [math.GM], 2017. See Table GW.n=6 p. 24.
%F A301421 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).
%o A301421 (PARI) lista(6, nn) \\ use pari script file in A301417; _Michel Marcus_, Apr 21 2018
%Y A301421 Cf. A301764, A024537, A195350, A301417, A301420, A301424.
%K A301421 nonn
%O A301421 1,2
%A A301421 _Gregory Gerard Wojnar_, Mar 20 2018
%E A301421 a(21) corrected by _Georg Fischer_, Aug 18 2021