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A152122
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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.
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0
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1, 1, 1, 5, 31, 121, 605, 2911, 13361, 64255, 302621, 1428031, 6770555, 31965701, 151200251, 715034375, 3380212751, 15984722176, 75579365455, 357361263031, 1689760311371, 7989708622205, 37778247366211, 178629122366311, 844620446404405, 3993667315453871
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Product_{k=1..(n-1)/2} Sum_{j=0..4} (2*cos(k*Pi/n))^(2*j).
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
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MATHEMATICA
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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]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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