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A076585 Let P(n,x) = Product_{k=1..n} polcyclo(k,x) where polcyclo(k,x) denotes the k-th cyclotomic polynomial. Sequence gives array of coefficients of P(n,x). 0

%I

%S 1,-1,1,0,-1,1,1,0,-1,-1,1,1,1,0,-1,-1,-1,1,2,3,3,2,0,-2,-3,-3,-2,-1,

%T 1,1,2,2,2,1,0,-1,-2,-2,-2,-1,-1,1,2,4,6,8,9,9,7,4,0,-4,-7,-9,-9,-8,

%U -6,-4,-2,-1,1,2,4,6,9,11,13,13,12,9,5,0,-5,-9,-12,-13,-13,-11,-9,-6,-4,-2,-1,1,2,4,7,11,15,20,24,27,28,27,23,17,9,0,-9

%N Let P(n,x) = Product_{k=1..n} polcyclo(k,x) where polcyclo(k,x) denotes the k-th cyclotomic polynomial. Sequence gives array of coefficients of P(n,x).

%C 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.

%e 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: 1,2,3,3,2,0,-2,-3,-3,-2,-1 is a segment in the sequence.

%e Triangle begins:

%e [1, -1]

%e [1, 0, -1]

%e [1, 1, 0, -1, -1]

%e [1, 1, 1, 0, -1, -1, -1]

%e [1, 2, 3, 3, 2, 0, -2, -3, -3, -2, -1]

%e [1, 1, 2, 2, 2, 1, 0, -1, -2, -2, -2, -1, -1]

%e [1, 2, 4, 6, 8, 9, 9, 7, 4, 0, -4, -7, -9, -9, -8, -6, -4, -2, -1]

%e ...

%o (PARI) row(n) = Vec(prod(k=1,n,polcyclo(k,x))); \\ _Michel Marcus_, May 24 2019

%K sign,tabf

%O 1,19

%A _Benoit Cloitre_, Oct 20 2002

%E Keyword tabf from _Michel Marcus_, May 24 2019

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Last modified January 28 20:57 EST 2022. Contains 350662 sequences. (Running on oeis4.)