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%I #12 Apr 11 2014 11:50:33
%S 1,1,1,-4,-3,5,0,13,21,-68,-55,89,0,233,377,-1220,-987,1597,0,4181,
%T 6765,-21892,-17711,28657,0,75025,121393,-392836,-317811,514229,0,
%U 1346269,2178309,-7049156,-5702887,9227465,0,24157817,39088169,-126491972,-102334155
%N a(n)=Product_{k=1..floor((n-1)/2)} (1 + 4*cos(k*Pi/n)^2)*(1 - 4*sin(k*Pi/n)^2).
%F Conjecture: a(2n) = A108196(n-1), n>=2. a(n) = (-1)^(n+1)*A000045(n) *A101675(n-1), n>0. G.f.: 1 -x*(x-1)*(x^2-x+1)*(1+x)^3 / ( (x^4-x^3+2*x^2+x+1)*(x^4+x^3+2*x^2-x+1) ). - _R. J. Mathar_, Mar 08 2011
%t f[n_] = Product[(1 + 4*Cos[k*Pi/n]^2)*(1 - 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[N[f[n]], {n, 0, 30}]; Round[%]
%o (PARI) a(n) = round(prod(k=1, floor((n-1)/2), (1+4*cos(k*Pi/n)^2)*(1-4*sin(k*Pi/n)^2))) \\ _Colin Barker_, Apr 11 2014
%Y Cf. A152189.
%K sign
%O 0,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 28 2008
%E More terms from _Colin Barker_, Apr 11 2014
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