%I #16 Feb 14 2021 05:52:56
%S 200,2916,80000,2775556,105125000,4115479104,163146144200,
%T 6498349262596,259309319120000,10354620147583716,413585320648104200,
%U 16521137110112348224,659981119616472888200,26365103950427540487396,1053246219256801250000000
%N a(n) = sqrt( Product_{j=1..n} Product_{k=1..6} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/6)^2) ).
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (77, -2002, 24596, -165165, 653835, -1598883, 2483481, -2483481, 1598883, -653835, 165165, -24596, 2002, -77, 1)
%F a(n) = 77*a(n-1) - 2002*a(n-2) + 24596*a(n-3) - 165165*a(n-4) + 653835*a(n-5) - 1598883*a(n-6) + 2483481*a(n-7) - 2483481*a(n-8) + 1598883*a(n-9) - 653835*a(n-10) + 165165*a(n-11) - 24596*a(n-12) + 2002*a(n-13) - 77*a(n-14) + a(n-15).
%F a(n) = 76*a(n-1) - 1926*a(n-2) + 22670*a(n-3) - 142495*a(n-4) + 511340*a(n-5) - 1087543*a(n-6) + 1395938*a(n-7) - 1087543*a(n-8) + 511340*a(n-9) - 142495*a(n-10) + 22670*a(n-11) - 1926*a(n-12) + 76*a(n-13) - a(n-14) - 2160.
%F G.f.: 4*(50*x - 3121*x^2 + 63967*x^3 - 616453*x^4 + 3219563*x^5 - 9827161*x^6 + 18330389*x^7 - 21405307*x^8 + 15754967*x^9 - 7241797*x^10 + 2026187*x^11 - 329569*x^12 + 28911*x^13 - 1182*x^14 + 16*x^15) / ((1 - x)*(1 - 7*x + x^2)*(1 - 6*x + x^2)*(1 - 3*x + x^2)* (1 - 42*x + 83*x^2 - 42*x^3 + x^4)*(1 - 18*x + 43*x^2 - 18*x^3 + x^4)). - _Vaclav Kotesovec_, Feb 14 2021
%o (PARI) default(realprecision, 120);
%o a(n) = round(sqrt(prod(j=1, n, prod(k=1, 6, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/6)^2))));
%Y Column k=6 of A341533.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Feb 14 2021