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A152191
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a(n)=Product_{k=1..floor((n-1)/2)} (1 + 4*cos(k*Pi/n)^2)*(1 - 4*sin(k*Pi/n)^2).
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0
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1, 1, 1, -4, -3, 5, 0, 13, 21, -68, -55, 89, 0, 233, 377, -1220, -987, 1597, 0, 4181, 6765, -21892, -17711, 28657, 0, 75025, 121393, -392836, -317811, 514229, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| 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
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MATHEMATICA
| 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[%]
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CROSSREFS
| Sequence in context: A085961 A175325 A205446 * A029934 A011397 A081665
Adjacent sequences: A152188 A152189 A152190 * A152192 A152193 A152194
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KEYWORD
| sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Nov 28 2008
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