OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..300
Dorin Andrica and Ovidiu Bagdasar, On some results concerning the polygonal polynomials, Carpathian Journal of Mathematics (2019) Vol. 35, No. 1, 1-11.
EXAMPLE
Denote P_n(x) = (x-1)...(x^n-1).
P_1(x) = x-1, hence a(1)=1.
P_2(x) = (x-1)*(x^2-1) = x^3-x^2-x+1, hence a(2)=2;
P_3(x) = (x-1)*(x^2-1)*(x^3-1) = x^6-x^5-x^4+x^2+x-1, hence a(3)=3;
P_4(x) = (x-1)*(x^2-1)*(x^3-1)*(x^4-1) = x^10 - x^9 - x^8+2x^5-x^2-x+1, hence a(4)=4.
MAPLE
a:= n-> add(`if`(i<0, 1, 0), i=[(p-> seq(coeff(p, x, i),
i=0..degree(p)))(expand(mul(x^i-1, i=1..n)))]):
seq(a(n), n=1..70); # Alois P. Heinz, Mar 29 2019
MATHEMATICA
Rest@ Array[Count[CoefficientList[Times @@ Array[x^# - 1 &, # - 1], x], _?(# < 0 &)] &, 71] (* Michael De Vlieger, Mar 29 2019 *)
PROG
(PARI) a(n) = #select(x->(x<0), Vec((prod(k=1, n, (x^k-1))))); \\ Michel Marcus, Apr 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ovidiu Bagdasar, Mar 25 2018
EXTENSIONS
Missing term 414 inserted by Alois P. Heinz, Mar 29 2019
STATUS
approved