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A122589 Expansion of 1/(1 - 11*x + 45*x^2 - 84*x^3 + 70*x^4 - 21*x^5 + x^6).

%I A122589 #26 Sep 08 2022 08:45:28
%S A122589 1,11,76,425,2109,9709,42504,179630,740025,2991495,11920740,46981740,
%T A122589 183579396,712493461,2750450981,10572046555,40495806764,154683305139,
%U A122589 589504177384,2242448706435,8517201473375,32309383853565
%N A122589 Expansion of 1/(1 - 11*x + 45*x^2 - 84*x^3 + 70*x^4 - 21*x^5 + x^6).
%C A122589 Previous name was: Sum_{n >= 0} a(n)*x^(2n) / 4^(n+6) = 1/(4096 - 11264*x^2 + 11520*x^4 - 5376*x^6 + 1120*x^8 - 84*x^10 + x^12).
%C A122589 Suggested by study of polynomials associated with the regular 13-gon.
%H A122589 G. C. Greubel, <a href="/A122589/b122589.txt">Table of n, a(n) for n = 0..1000</a>
%H A122589 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-45,84,-70,21,-1).
%F A122589 G.f.: 1/(1 - 11*x + 45*x^2 - 84*x^3 + 70*x^4 - 21*x^5 + x^6). - _Colin Barker_, Oct 16 2013
%p A122589 A122589:= proc(n) coeftayl(1/(4096-11264*x^2+11520*x^4-5376*x^6+1120*x^8-84*x^10 +x^12), x=0,2*n); %*2^(2*n+12); end: seq(A122589(n), n=0..30); # _R. J. Mathar_, Sep 21 2007
%t A122589 m=12; p[x_]:= ExpandAll[x^m*ChebyshevU[m, 1/x]]; Table[ SeriesCoefficient[ Series[2^(n+m-1)*x/p[x], {x,0,30}], n], {n,1,30,2}]
%o A122589 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-11*x+45*x^2 -84*x^3+70*x^4-21*x^5+x^6) )); // _G. C. Greubel_, Nov 29 2021
%o A122589 (Sage)
%o A122589 def A122589_list(prec):
%o A122589     P.<x> = PowerSeriesRing(ZZ, prec)
%o A122589     return P( 1/(1-11*x+45*x^2-84*x^3+70*x^4-21*x^5+x^6) ).list()
%o A122589 A122589_list(30) # _G. C. Greubel_, Nov 29 2021
%Y A122589 Cf. A005021, A094256, A122588.
%K A122589 nonn,easy
%O A122589 0,2
%A A122589 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 19 2006
%E A122589 Edited by _N. J. A. Sloane_, Oct 02 2006
%E A122589 More terms from _R. J. Mathar_, Sep 21 2007
%E A122589 New name from _Colin Barker_, Oct 16 2013