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%I #16 Jan 07 2021 04:55:13
%S 1,1,1,13,7,76,39,421,217,2353,1216,13201,6825,74101,38311,415948,
%T 215047,2334781,1207089,13105441,6775552,73562593,38032081,412916701,
%U 213479175,2317756876,1198287271,13009880533,6726147337,73026206161
%N a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*sin(k*Pi/n)^2 + 16*sin(k*Pi/n)^4).
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,7,0,-9,0,7,0,-1).
%F G.f.: (x^8 - x^7 - 8*x^6 - 6*x^5 + 9*x^4 + 6*x^3 - 6*x^2 + x + 1) / ((x^4 - x^3 - 3*x^2 - x + 1)*(x^4 + x^3 - 3*x^2 + x + 1)). - _Colin Barker_, Jan 05 2014
%t f[n_] = Product[(1 + 4*Sin[k*Pi/n]^2 + 16*Sin[k*Pi/n]^4), {k, 1, Floor[(n - 1)/2]}]; a = Table[f[n], {n, 0, 30}]; Round[a]; FullSimplify[ExpandAll[a]]
%o (PARI) Vec((x^8-x^7-8*x^6-6*x^5+9*x^4+6*x^3-6*x^2+x+1)/((x^4-x^3-3*x^2-x+1)*(x^4+x^3-3*x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Jan 05 2014
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 26 2008