A076585 - OEIS

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).

1, 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, 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, -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

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OFFSET

0,20

COMMENTS

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.

LINKS

Alois P. Heinz, Rows n = 0..60, flattened

EXAMPLE

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.

Triangle begins:

[1]

[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]

[1, 1, 2, 2, 2, 1, 0, -1, -2, -2, -2, -1, -1]