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%I #16 Mar 29 2019 17:06:32
%S 1,2,3,3,6,6,9,13,16,18,21,27,34,32,42,47,54,62,73,79,85,96,104,113,
%T 123,140,150,171,174,190,200,211,234,240,263,275,301,304,322,351,368,
%U 396,413,455,451,470,487,499,531,540,592,585,631,630,687,691,734,774,793,863
%N a(n) is the number of positive coefficients of the polynomial (x-1)*(x^2-1)*...*(x^n-1).
%D D. Andrica and O. Bagdasar, On some results concerning the polygonal polynomials, submitted to Carpathian Journal of Mathematics (2018).
%H Michael De Vlieger, <a href="/A301703/b301703.txt">Table of n, a(n) for n = 1..300</a>
%H Dorin Andrica, Ovidiu Bagdasar, <a href="http://hdl.handle.net/10545/623501">On some results concerning the polygonal polynomials</a>, Carpathian Journal of Mathematics (2019) Vol. 35, No. 1, 1-11.
%e Denote P_n(x) = (x-1)...(x^n-1).
%e P_1(x) = x-1, hence a(1)=1.
%e P_2(x) = (x-1)*(x^2-1) = x^3-x^2-x+1, hence a(2)=2;
%e 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;
%e 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)=3.
%p a:= n-> nops(select(x-> x>0, [(p-> seq(coeff(p, x, i),
%p i=0..degree(p)))(expand(mul(x^i-1, i=1..n)))])):
%p seq(a(n), n=1..60); # _Alois P. Heinz_, Mar 29 2019
%t Table[Count[CoefficientList[Expand[Times@@(x^Range[n]-1)],x],_?(#>0&)],{n,60}] (* _Harvey P. Dale_, Feb 10 2019 *)
%o (PARI) a(n) = #select(x->(x>0), Vec((prod(k=1, n, (x^k-1))))); \\ _Michel Marcus_, Apr 02 2018
%Y Cf. A231599: a(n) is the number of positive coefficients in row n.
%K nonn,easy
%O 1,2
%A _Ovidiu Bagdasar_, Mar 25 2018
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