A152122 - OEIS

%I #9 Apr 01 2016 15:04:39

%S 1,1,1,5,31,121,605,2911,13361,64255,302621,1428031,6770555,31965701,

%T 151200251,715034375,3380212751,15984722176,75579365455,357361263031,

%U 1689760311371,7989708622205,37778247366211,178629122366311,844620446404405,3993667315453871

%N a(n) = Product_{k=1..(n-1)/2} 1 + 4*cos(k*Pi/n)^2 + 16*cos(k*Pi/n)^4 + 64*cos(k*Pi/n)^6 + 256*cos(k*Pi/n)^8.

%F a(n) = Product_{k=1..(n-1)/2} Sum_{j=0..4} (2*cos(k*Pi/n))^(2*j).

%F Empirical g.f.: (1 -15*x^2 -36*x^3 +31*x^4 +130*x^5 -81*x^6 -184*x^7 +265*x^8 -26*x^9 -149*x^10 +60*x^11 +59*x^12 -14*x^13 -15*x^14 -2*x^15 +x^16) / (1 -x -15*x^2 -25*x^3 +45*x^4 +95*x^5 -115*x^6 -105*x^7 +265*x^8 -105*x^9 -115*x^10 +95*x^11 +45*x^12 -25*x^13 -15*x^14 -x^15 +x^16). - _Colin Barker_, Apr 01 2016

%t a = Table[Product[1 + 4*Cos[k*Pi/n]^2 + 16*Cos[k*Pi/n]^4 + 64*Cos[k*Pi/n]^6 + 256*Cos[k*Pi/n]^8, {k, 1, (n - 1)/2}], {n, 0, 30}]; Round[%] FullSimplify[ExpandAll[a]]

%o (PARI) a(n) = round(prod(k=1, (n-1)/2, 1 + 4*cos(k*Pi/n)^2 + 16*cos(k*Pi/n)^4 + 64*cos(k*Pi/n)^6 + 256*cos(k*Pi/n)^8)) \\ _Colin Barker_, Apr 01 2016

%K nonn

%O 0,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 24 2008

%E Name and formula corrected by _Colin Barker_, Apr 01 2016