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A076584
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Let P(n,x) = Product_{k=1..n} polcyclo(k,x) where polcyclo(k,x) denotes the k-th cyclotomic polynomial. Sequence gives the maximum value of coefficients of P(n,x).
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0
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1, 1, 1, 1, 3, 2, 9, 13, 28, 22, 174, 143, 1421, 1179, 965, 1627, 22543, 19720, 311514, 273894, 236320, 209255, 4127583, 3734824, 16283658, 14694118, 39214357, 35681217, 915568753, 847646751, 23431024516, 43093548356, 39165894190
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OFFSET
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1,5
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COMMENTS
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The degree of P(n,x) is phi(1) + phi(2) + ... + phi(n) = A002088(n) and if c(n,i) denotes the coefficient of x^i in P(n,x): c(n,i) + c(n, A002088(n) - i) = 0.
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LINKS
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EXAMPLE
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P(5,x) = x^10 + 2*x^9 + 3*x^8 + 3*x^7 + 2*x^6 - 2*x^4 - 3*x^3 - 3*x^2 - 2*x - 1, hence a(5)=3.
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PROG
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(PARI) a(n)=vecmax(vector(sum(k=1, n, eulerphi(k))+1, i, polcoeff(prod(i=1, n, polcyclo(i)), i-1)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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