

A076585


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


0



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

1,19


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

Table of n, a(n) for n=1..99.


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, 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]
...


PROG

(PARI) row(n) = Vec(prod(k=1, n, polcyclo(k, x))); \\ Michel Marcus, May 24 2019


CROSSREFS

Sequence in context: A198197 A203400 A077869 * A323186 A022906 A285408
Adjacent sequences: A076582 A076583 A076584 * A076586 A076587 A076588


KEYWORD

sign,tabf


AUTHOR

Benoit Cloitre, Oct 20 2002


EXTENSIONS

Keyword tabf from Michel Marcus, May 24 2019


STATUS

approved



