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%I #14 Sep 08 2022 08:45:39
%S 1,1,1,16,55,355,1888,9829,57145,294064,1683055,8893147,49635520,
%T 267601933,1472118817,8012384080,43823300455,239288418067,
%U 1306681029664,7139564615413,38980858167625,212971742938096,1162967620577311
%N Quartic product sequence: a(n) = Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=12 and q = 3*4^3.
%C Limiting ratio at n=30 equals 5.461866286689612.
%C Exact value of this limit is (1 + sqrt(205) + sqrt(2*(7+sqrt(205))))/4 = 5.46185461429652018724... - _Vaclav Kotesovec_, Nov 30 2012
%H Vincenzo Librandi, <a href="/A152096/b152096.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=3*4 and q = 3*4^3.
%F G.f.: 1 + x*(1-12*x^2)/(1-x-27*x^2-12*x^3+144*x^4). - _Vaclav Kotesovec_, Nov 30 2012
%t With[{m = 3*4, q = 3*4^3}, Table[Round[Product[1 + m*Cos[k*Pi/n]^2 + q*Cos[k*Pi/n]^4, {k, 1, (n-1)/2}]], {n, 0, 30}]] (* modified by _G. C. Greubel_, May 15 2019 *)
%t CoefficientList[Series[1+x*(1-12*x^2)/(1-x-27*x^2-12*x^3+144*x^4), {x, 0, 22}], x] (* _Vaclav Kotesovec_, Nov 30 2012 *)
%o (PARI) my(x='x+O('x^30)); Vec(1 + x*(1-12*x^2)/(1-x-27*x^2-12*x^3 +144*x^4)) \\ _G. C. Greubel_, May 15 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1 + x*(1-12*x^2)/(1-x-27*x^2-12*x^3+144*x^4) )); // _G. C. Greubel_, May 15 2019
%o (Sage) (1 + x*(1-12*x^2)/(1-x-27*x^2-12*x^3+144*x^4)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 15 2019
%K nonn
%O 0,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 24 2008
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